They travelled for twenty days during which they shortened their prayers. Do they have to make them up?

Firstly: 

The majority
of scholars are of the view that a traveller may avail himself of the
concessions of travel so long as he is not staying in the place to which he
has gone for four or more days, whether he travels for work, medical
treatment, a vacation or any other reason. 

See the
answer to question no. 21091. 

Ibn Qudaamah
(may Allaah have mercy on him) said: The well known view of Ahmad (may
Allaah have mercy on him) is that the period during which the traveller must
perform his prayers in full with the intention of staying is a period in
which there are more than twenty-one prayers. And it was narrated from him
that if he intends to stay for more than four days he must perform his
prayers in full, but if he intends to stay less than that, he may shorten
them. This is also the view of Maalik and al-Shaafa’i. End quote from
al-Mughni (2/65). 

It says in
Fataawa al-Lajnah al-Daa’imah (8/109): the basic principle is that
the traveller who is actually travelling is the one who is granted a
concession allowing him to shorten the four-rak’ah prayers, because Allaah
says (interpretation of the meaning): 

“And when
you (Muslims) travel in the land, there is no sin on you if you shorten
As‑Salaah (the prayer)”

[al-Nisa’
4:101] 

and Ya’la
ibn Umayyah said: I said to ‘Umar ibn al-Khattaab (may Allaah be pleased
with him): “ ‘And when you (Muslims) travel in the land, there is no sin
on you if you shorten As‑Salaah (the prayer) if you fear that the
disbelievers may put you in trial (attack you),’” He said: I wondered
the same thing as you, and I asked the Messenger of Allaah (peace and
blessings of Allaah be upon him) about it, and he said: “It is a charity
that Allaah has bestowed upon you, so accept His charity.” Narrated by
Muslim. 

The one who
stays in a place for four days and nights or less also comes under the
ruling of the traveller who is actually travelling, because it is proven in
the hadeeth of Jaabir and Ibn ‘Abbaas (may Allaah be pleased with them) that
the Prophet (peace and blessings of Allaah be upon him) came to Makkah
on the fourth of Dhu’l-Hijjah for the Farewell Pilgrimage, and he
(peace and blessings of Allaah be upon him) stayed for the fourth, fifth,
sixth and seventh, and he prayed Fajr in al-Abtah on the eighth day, and he
shortened his prayers during those days. He had formed the intention to
stay, as is well known. So everyone who travels and intends to stay for this
length of time that the Prophet (peace and blessings of Allaah be upon
him) stayed, or less, may shorten his prayers. Whoever intends to stay
longer than that should offer the prayers in full, because he does not come
under the heading of a traveler. 

But if a
person stays for longer than four days during his trip and has not formed
the intention to stay, rather he has resolved that when he has finished his
business he will go back, like one who stays in a place to engage in jihad
against the enemy, or has been detained by the authorities or by sickness,
but he has resolved that when the jihad ends with victory or a peace treaty,
or the sickness or enemy power that is keeping him there ends, or he sells
all his goods and so on, he will go back, then he is regarded as a
traveller, and he may shorten the four-rak’ah prayers, even if that period
is long, because it is proven that the Prophet (peace and blessings of
Allaah be upon him) stayed in Makkah during the year of the Conquest for
nineteen days, during which he shortened his prayers, and he stayed in
Tabook for twenty days to fight the Christians, and he led his companions in
shortened prayers, because he had not resolved to stay, rather his intention
was to leave once he had finished his business. End quote. 

Secondly: 

The Sahaabah
(may Allaah be pleased with them) did not travel for a vacation for six
months as mentioned in the question. Rather they would travel for jihad for
the sake of Allaah, or to seek knowledge, or to seek a halaal provision, and
other religious and worldly interests, such as Ibn ‘Umar (may Allaah be
pleased with him) who stayed in Azerbaijan for six months, and snow kept him
from entering, and he shortened his prayers. 

Thirdly: 

You do not
have to make up the prayers that you shortened during this time, because it
is possible that you may come under the category of travelling. The Standing
Committee was asked about a person who was sent by Saudi to Germany, who
stayed there for nearly one and half years and he shortened his prayer. They
replied: 

You do not
have to make up the prayers that you shortened or delayed or joined with
other prayers, because it is possible that you may come under the heading of
travelling. But in the future you should pray the four-rak’ah prayers in
full and offer every prayer on time, because the ruling of travel no longer
applies to you, because you have resolved to stay, and you have resolved to
stay for more than four days. So you have to pray in congregation if
possible, and do not pray alone.   

End quote
from Fataawa al-Lajnah al-Daa’imah (8/155) 

And Allaah
knows best.