He offers all the obligatory prayers in the mosque except for Fajr. What is the ruling on that?

You should note that Allaah has blessed you by enabling you
to offer the prayers in the mosque with the congregation, to stand before
Allaah in His house and establish this great ritual of Islam and to do
that which Allaah has enjoined upon you. There is nothing that is more
beloved to Allaah than fulfilment of what He has enjoined. We have already
discussed the obligation of praying in congregation in question no.

8918. 

With regard to what you say about praying Fajr in your house,
this is a sin for which you must repent to Allaah, and it is a problem from
which you are suffering and we ask Allaah to help you to overcome it. That
is because the evidence which indicates that it is obligatory to pray in
congregation does not apply only to some prayers and not others, rather it
is general in meaning and applies to all the prayers, the first of which is
Fajr, about which you are asking. 

How can you feel comfortable about not praying Fajr in
congregation and depriving yourself of complete light on the Day of
Resurrection? Abu Dawood (561), al-Tirmidhi (223) and Ibn Maajah (781)
narrated from Buraydah (may Allaah be pleased with him) that the Prophet
(peace and blessings of Allaah be upon him) said: “Give glad tidings to
those who walk to the mosques in the dark, of perfect light on the Day of
Resurrection.” Classed as saheeh by al-Albaani in Saheeh al-Targheeb. 

How can you feel comfortable about not praying Fajr in
congregation and depriving yourself of meeting the angels and their
testifying for you before your Lord? Al-Bukhaari (555) and Muslim (632)
narrated from Abu Hurayrah (may Allaah be pleased with him) that the
Messenger of Allaah (peace and blessings of Allaah be upon him) said:
“Angels come to you in succession, night and day, and they meet at Fajr
prayer and ‘Asr prayer, then those who stayed among you overnight ascend and
[Allaah] asks them – although He knows better about them – ‘How did you
leave My slaves?’ and they say, ‘We left them when they were praying and we
came to them when they were praying.’” 

How can you feel comfortable about not praying Fajr in
congregation and depriving yourself of the reward of spending half the night
in prayer? Muslim narrated in his Saheeh (656) that ‘Uthmaan (may
Allaah be pleased with him) said: I heard the Messenger of Allaah
(peace and blessings of Allaah be upon him) say: “Whoever prays ‘Isha’ in
congregation, it is as if he spent half the night in prayer, and whoever
prays Fajr in congregation, it is as if he spent the whole night in
prayer.” 

According to a report narrated by Abu Dawood (555) and
al-Tirmidhi (221): “Whoever prays ‘Isha’ in congregation, it is as if he
spent half the night in prayer, and whoever prays ‘Isha’ and Fajr in
congregation, it is as if he spent the (whole) night in prayer.” 

How can you feel comfortable about not praying Fajr in
congregation and depriving yourself of the protection of Allaah? It was
narrated that Abu Bakrah (may Allaah be pleased with him) said: The
Messenger of Allaah (peace and blessings of Allaah be upon him) said:
“Whoever prays Fajr with the congregation will be under the protection of
Allaah, and whoever violates this protection of Allaah, Allaah will throw
him into the Fire on his face.” Al-Haythami said in Majma’ al-Zawaa’id:
This was narrated by al-Tabaraani in al-Kabeer in a hadeeth; this is
its wording and its men are the men of saheeh; it was also classed as saheeh
by al-Albaani in Saheeh al-Targheeb. 

The origin of this hadeeth is in Saheeh Muslim, in the
chapter entitled The virtue of praying ‘Isha’ and Fajr in congregation
(657). “Whoever violates the protection of Allaah,” means by harming and
offending the believer who prayed Fajr in congregation. 

How can you feel comfortable about not praying Fajr in
congregation when the Prophet (peace and blessings of Allaah be upon
him) has told us that feeling that it is too burdensome to pray Fajr in
congregation is the sign of the hypocrites? Al-Bukhaari (657) and Muslim
(651) narrated that Abu Hurayrah (may Allaah be pleased with him) said: The
Messenger of Allaah (peace and blessings of Allaah be upon him) said:
“The most burdensome of prayers for the hypocrites are ‘Isha’ and Fajr. If
only they knew what (reward) there is in them, they would come to them even
if they had to crawl. I was thinking of ordering that the call to prayer be
given, then I would tell a man to lead the people in prayer, then I would
set out with some men carrying bundles of wood and go to people who do not
attend the prayer, and burn their houses down with them inside.” 

‘Abd-Allaah ibn ‘Umar (may Allaah be pleased with him) said:
“When we noticed that a man was not present at Fajr and ‘Isha’ prayer, we
would think badly of him.” Narrated by al-Haakim in al-Mustadrak,
764, and elsewhere; he classed it as saheeh according to the conditions of
the two shaykhs (al-Bukhaari and Muslim), and al-Dhahabi and al-Albaani
agreed with him. 

The Muslim who is keen to attend the prayers in congregation,
as you describe yourself, would not feel comfortable, in sha Allaah, to miss
praying Fajr in congregation, after hearing what the Prophet (peace and
blessings of Allaah be upon him) said about that. 

May Allaah help us and you to do that which He loves and
which pleases Him.