What is meant by dhikr and du‘aa’ at the end of the prayer?

Firstly: 

“At the end of the prayer” may mean after it, following it,
or in the last part of it. 

There are several hadeeths which encourage dhikr and du‘aa’
at the end of the prayers, such as the following: 

1.

The report narrated by al-Bukhaari (6330) and Muslim (594)
from al-Mugheerah ibn Shu‘bah (may Allah be pleased with him), according to
which the Messenger of Allah (blessings and peace of Allah be upon him) used
to say at the end of every prayer after saying the salaam: Laa ilaaha
ill-Allaah wahdahu laa shareeka lah, lahu’l-mulk wa lahu’l-hamd wa huwa ‘ala
kulli shay’in qadeer. Allaahumma laa maani‘ lima a‘tayta wa laa mu‘ti lima
mana‘ta wa la yanfa‘ dhaa’l-jadd minka al-jadd  (There is no god but
Allaah Alone, with no partner or associate, His is the sovereignty and to
Him be praise, and He is Able to do all things. O Allaah, none can withhold
what You give and none can give what You withhold, and no wealth or majesty
can benefit anyone for from You is all wealth and majesty). 

2.

The report narrated by al-Bukhaari (6329) from Abu Hurayrah
(may Allah be pleased with him): They said: O Messenger of Allah, the
wealthy have attained exclusively the high ranks and eternal blessing (in
Paradise). He said: How is that? They said: They pray as we pray, and they
strive in jihad as we strive, and they spend from the surplus of their
wealth, but we have no wealth. He said: “Shall I not tell you of something
by means of which you will catch up with those who have gone before you and
will go ahead of those who come after you, and no one could achieve what you
achieve except one who does what you do. At the end of every prayer, glorify
Allah (by saying Subhaan Allah) ten times, and praise Him (by saying
al-hamdu Lillah) ten times, and magnify Him (by saying Allahu
akbar) ten times. 

Al-Bukhaari (843) narrated: “Glorify Allah (by saying
Subhaan Allah), praise Him (by saying al-hamdu Lillah), and
magnify Him (by saying Allahu akbar) thirty-three times after each
prayer.” 

Muslim (595) narrated: “Glorify Allah (by saying Subhaan
Allah), praise Him (by saying al-hamdu Lillah), and magnify Him
(by saying Allahu akbar) thirty-three times at the end of each
prayer.” 

3.

Muslim (596) narrated from Ka‘b ibn ‘Ujrah (may Allah be
pleased with him) that the Messenger of Allah (blessings and peace of Allah
be upon him) said: “Dhikrs at the end of the prayer, the one who says them
or does them at the end of each obligatory prayer will not be disappointed:
thirty-three tasbeehahs, thirty-three tahmeedahs and thirty-four takbeerahs.” 

What is meant by “at the end of the prayer” in these hadeeths
is immediately after the prayer, that is, after the salaam, as is stated
clearly in some reports. The same is mentioned in the reports which speak of
reciting Aayat al-Kursiy and the Mu‘awwidhaat at the end of the prayer. What
is meant is after the salaam. 

4.

Abu Dawood (1522) narrated from Mu‘aadh ibn Jabal (may Allah
be pleased with him) that the Messenger of Allah (blessings and peace of
Allah be upon him) took him by the hand and said: “O Mu‘aadh, by Allah
verily I love you, by Allah verily I love you.” Then he said: “I urge you, O
Mu‘aadh, never to stop saying at the end of every prayer: Allahumma
a‘inni ‘ala dhikrika wa shukrika wa husni ‘ibaadatika (O Allah, help me
to remember You, give thank to You and worship You properly).”

Classed as saheeh by al-Albaani in
Saheeh Abi Dawood 

An-Nasaa’i (1303) narrated it as follows: “Do not neglect to
say in every prayer, Rabbiy a‘inni ‘ala dhikrika wa shukrika wa husni
‘ibaadatika (My Lord, help me to remember You, give thank to You and
worship You properly).

Classed as saheeh by al-Albaani in
Saheeh an-Nasaa’i. 

What is meant by “at the end of the prayer (dibr as-salaah)”
here is in the last part of the prayer before the salaam, because dibr
ash-shay’ (lit. the end of a thing) is part of it. This is confirmed by
the words in the report of an-Nasaa’i: “in every prayer”. 

Ibn al-Qayyim (may Allah have mercy on him) said in Zaad
al-Ma‘aad (1/294): “At the end of the prayer” may be understood as
meaning before the salaam or after it. Our shaykh [i.e., Ibn Taymiyah]
regarded it as more likely that it is before the salaam. I asked him  about
that and he said: Dibr kulli shay’ (the end of everything) is part of it,
like the dibr (rear end) of an animal. End quote. 

5.

at-Tirmidhi (3499) narrated that Abu Umaamah (may Allah be
pleased with him) said: It was said: O Messenger of Allah, what du‘aa’
(supplication) is most likely to be heard (and responded to)? He said:
“(That which is offered) in the last part of the night and at the end of the
prescribed prayers.”

This hadeeth was classed as hasan by at-Tirmidhi and by
al-Albaani in Saheeh at-Tirmidhi. 

What appears to be the case is that what is meant by “at the
end of the prayer” here means before the salaam. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
What appears to be the case is that what is meant by “at the end of the
prescribed prayers” in the hadeeth of Abu Umaamah – if it is saheeh –is: in
the last part of the prayer. End quote. 

Majmoo‘ Fataawa Ibn ‘Uthaymeen,
13/268 

The scholars noted concerning this that in the texts which
mention the end of the prayer, if it is dhikr (such as saying Subhaan
Allah, al-hamdu Lillah, Allahu akbar, or reciting Aayat al-Kursiy
and the Mu‘awwidhaat), then what is meant by the end of the prayer in this
case is after the prayer; if it is du‘aa’ (supplication), then what is meant
by at the end of the prayer is in the last part of it, i.e., before the
salaam. 

But if there is a report to indicate that a particular du‘aa’
should be said after the salaam, such as when the Prophet (blessings and
peace of Allah be upon him) said: “Ask for forgiveness (by saying
Astaghfirullah) three times,” this is a du‘aa’, but the Sunnah indicates
that it should be said after the salaam. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked: 

What is meant by “at the end of the prayer” in the hadeeths
which encourage saying du‘aa’ or dhikr at the end of each prayer? Is it the
last part of the prayer or after the salaam? 

He replied: 

The phrase “the end of the prayer” may be applied to the last
part of it before the salaam, or it may be applied to what comes immediately
after the salaam. There are saheeh hadeeths that mention that, most of which
indicate that what is meant is the last part of the prayer before the salaam
if it has to do with du‘aa’, such as the hadeeth of Ibn Mas‘ood, in which
the Messenger (blessings and peace of Allah be upon him) taught him the
tashahhud, then he said: “Then let him choose whatever du‘aa’ he likes and
say it.” And according to another version he said, “Let him choose after
asking whatever he wants.” (saheeh – agreed upon). 

Another example is the hadeeth of Mu‘aadh in which the
Prophet (blessings and peace of Allah be upon him) said to him: “Do not
neglect to say at the end of every prayer: Allahumma a‘inni ‘ala dhikrika
wa shukrika wa husni ‘ibaadatika (O Allah, help me to remember You, give
thank to You and worship You properly).”

Narrated by Abu Dawood, at-Tirmidhi and an-Nasaa’i with a
saheeh isnaad. 

Another example is the hadeeth narrated by al-Bukhaari (may
Allah have mercy on him) from Sa‘d ibn Abi Waqqaas (may Allah be pleased
with him) who said: The Prophet (blessings and peace of Allah be upon him)
used to say at the end of every prayer: “Allaahumma inni a‘oodhu bika min
al-bukhl, wa a‘oodhu bika min al-jubn, wa a‘oodhu bika min an uradda ila
ardhal il-‘umr, wa a‘oodhu bika min fitnat ad-dunya wa min ‘adhaab al-qabr
(O Allah, I seek refuge in You from miserliness, and I seek refuge in You
from cowardice, and I seek refuge in You from reaching feeble old age, and I
seek refuge in You from the trials of this world, and I seek refuge in You
from the torment of the grave. 

With regard to the adhkaar that have been narrated, the
saheeh hadeeths indicate that they are to be recited at the end of the
prayer after the salaam. An example of that is to say after saying the
salaam: “Astaghfirullah, astaghfirullah, astaghfirullah. Allaahumma anta
al-salaam wa minka al-salaam tabaarakta ya dhaa’l-jalaali wa’l-ikraam (I
ask Allaah for forgiveness, I ask Allaah for forgiveness, I ask Allaah for
forgiveness. O Allaah, You are the One Who is free from all defects and
deficiencies and from You is all peace, blessed are You, O Possessor of
majesty and honour), whether he was the imam or praying behind the imam or
praying on his own. Then after that the imam should turn to face the
congregation, and the imam, the one who prayed behind the imam and the one
who prayed on his own should say, after that dhikr and prayer for
forgiveness: Laa ilaaha ill-Allaah wahdahu laa shareeka lah, lahu’l-mulk
wa lahu’l-hamd wa huwa ‘ala kulli shay’in qadeer. Laa hawla wa laa quwwata
illa Billaah wa laa na‘budu illaa iyyaah. Lahu’l-ni‘mah wa lahu’l-fadl wa
lahu’l-thanaa’ al-hasan. Laa ilaaha ill-Allaah mukhliseena lahu’l-deena wa
law kariha’l-kaafiroon. Allaahumma laa maani‘ lima a‘tayta wa laa mu‘ti lima
mana‘ta wa la yanfa‘ dhaa’l-jadd minka al-jadd  (There is no god but
Allaah Alone, with no partner or associate His is the sovereignty and to Him
be praise, and He is Able to do all things. There is no power and no
strength except with Allaah, and we worship none but Him.  From Him (alone)
come all blessings and favours, and all good praise is due to Him. There is
no god but Allaah and we make our worship purely for Him (alone) however
much the disbelievers may hate that. O Allaah, none can withhold what You
give and none can give what You withhold, and no wealth or majesty can
benefit anyone for from You is all wealth and majesty). 

It is mustahabb for the Muslim, male or female, to recite
this dhikr after each of the five daily prayers, then to glorify Allah (by
saying Subhaan Allah), praise Him (by saying al-hamdu Lillah),
and magnify Him (by saying Allahu akbar) thirty-three times, then to
complete one hundred by saying: Laa ilaaha ill-Allaah wahdahu laa shareeka
lah, lahu’l-mulk wa lahu’l-hamd wa huwa ‘ala kulli shay’in qadeer (There is
no god but Allaah Alone, with no partner or associate His is the sovereignty
and to Him be praise, and He is Able to do all things).

All of that is proven in hadeeths from the Messenger of Allah
(blessings and peace of Allah be upon him). After that it is mustahabb to
recite Aayat al-Kursiy once, quietly, and to recite Qul Huwa Allahu Ahad
(Soorat al-Ikhlaas) and al-Mu‘awwidhatayn once, quietly, except in the case
of Maghrib and Fajr, when it is mustahabb to repeat the recitation of the
three soorahs mentioned, three times. It is also mustahabb for the Muslim,
male or female, to say after praying Maghrib and Fajr: Laa ilaaha
ill-Allaah wahdahu laa shareeka lah, lahu’l-mulk wa lahu’l-hamd yuhyi wa
yumeet wa huwa ‘ala kulli shay’in qadeer (there is no God but Allaah
alone, with no partner or associate, His is the Dominion and to Him be
praise, He gives life and gives death, and He has power over all things) ten
times in addition to what is mentioned above, before reciting Aayat
al-Kursiy and before reciting the three soorahs mentioned above, in
accordance with the saheeh hadeeths that have been narrated concerning that.
End quote. 

Majmoo‘ Fataawa Ibn Baaz,
11/194 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

If one ponders this matter it will become clear that what is
connected to the end of the prayer, if it is dhikr it comes after the prayer
and if it is du‘aa’ it comes in the last part of the prayer. 

With regard to the former, Allah, may He be exalted, has made
the time after the prayer a time for dhikr, as He says (interpretation of
the meaning): “When you have finished As-Salat (the prayer –
congregational), remember Allah standing, sitting down, and lying down on
your sides” [an-Nisa’ 4:103]. And the Sunnah explains what is mentioned
in general terms in this verse of dhikr, such as when the Prophet (blessings
and peace of Allah be upon him) said: “The one who glorifies Allah (by
saying Subhaan Allah) at the end of every prayer thirty-three times…”
Each text that mentions dhikr at the end of the prayer is to be understood
as referring to after the prayer, in accordance with this verse. 

With regard to the latter, the Prophet (blessings and peace
of Allah be upon him) regarded the time after the final tashahhud as a time
for du‘aa’. So every text that mentions du‘aa’ at the end of the prayer is
to be understood as referring to the last part of it, so that the du‘aa’
will be at the point where the Prophet (blessings and peace of Allah be upon
him) taught us to offer du‘aa’, unless interpreting the text in this manner
is impossible or unlikely, according to the context, in which case it is to
be understood as indicated by the context. End quote. 

Majmoo‘ Fataawa Ibn ‘Uthaymeen,
13/268 

Secondly: 

It is not prescribed to raise the hands when saying du‘aa’
after the prayer, because that was not narrated from the Prophet (blessings
and peace of Allah be upon him). It says in Fataawa al-Lajnah ad-Daa’imah
(7/103): When saying du‘aa’ after the obligatory prayer it is not Sunnah to
raise the hands, whether that is done by the imam on his own or the one who
prayed behind the imam on his own, or by both of them. Rather that is an
innovation, because it was not narrated from the Prophet (blessings and
peace of Allah be upon him) or from his Companions (may Allah be pleased
with them). As for saying du‘aa’ without doing that (raising the hands),
there is nothing wrong with it, because there are some hadeeths that mention
that. End quote. 

See also the
answer to question no. 21976
and 7886 

And Allah knows best.