The Hadith in mention:
عَنْ أَنَسِ بْنِ مَالِكٍ قَالَ قَالَ رَسُولُ اللَّهِ -صلى الله عليه وسلم- « مَنْ صَلَّى الْغَدَاةَ فِى جَمَاعَةٍ ثُمَّ قَعَدَ يَذْكُرُ اللَّهَ حَتَّى تَطْلُعَ الشَّمْسُ ثُمَّ صَلَّى رَكْعَتَيْنِ كَانَتْ لَهُ كَأَجْرِ حَجَّةٍ وَعُمْرَةٍ
Anas bin Malik narrated that the Messenger of Allah said: “Whoever prays Fajr in congregation, then sits remembering Allah until the sun has risen, then he prays two Rak’ah, then for him is the reward like that of a Hajj and Umrah.” He said: “The Messenger of Allah said: ‘Complete, complete, complete.'”
[Reported by at-Tirmidhi and graded Hasan by al-Albani in Saheeh Tirmidhi no. 586]
Also Shaikh Bin Baz rahimahullah graded it Hasan li-Ghayri and mentioned that it should be prayed 15-20 minutes afterwards:
57- What is the authenticity of the Hadith “Whoever sits after the Fajr Prayer and remembers Allah until the sun rises, then offers two Rak`ahs, he will have a reward like that of making a full Hajj.”?
What is the authenticity of the Hadith, “Whoever sits after the Fajr Prayer and remembering Allah until the sun rises, then offers two Rak`ahs, he will have a reward like that of making Hajj and ‘Umrah, complete, complete, complete”?
This Hadith was related through some satisfactory chains of transmission. Thus, it is regarded as Hasan Li Ghayrih (A Hadith is judged as Good by virtue of another Hadith when its weakness is so minor that it can be raised through another chain to the level of the Good Hadith). It is most recommended to offer this supererogatory Salah after the sun has already risen to the height of a spear, i.e., approximately fifteen or twenty minutes after sunrise.
A person can busy reading the Quran unitl then or do any other dhikr:
A man sits in the Masjid (mosque) to recite Qur’an after offering Fajr (Dawn) Prayer until sunrise, then he prays two Rak`ahs (unit of Prayer). However, some people denied his deed and said ‘It is not permissible because it is the tradition of the worshippers of the Sun.’ Please, advise! May Allah reward you!
Whoever sits in the Masjid to recite Qur’an and the formulas of Adhkar (invocations and remembrances said at certain times on a regular basis) after offering Fajr Prayer until sunrise is clear and the time when Salah is forbidden is over and prays two Rak`ahs or what he could, he indeed does a good and great deed. His act agrees with the Sunnah and is rewarded, In sha’a-Allah (if Allah wills). In support of this, it is reported on the authority of Anas ibn Malik (may Allah be pleased with him) that the Messenger of Allah said: Whoever prays the morning prayer in congregation then sits remembering Allah until the sun rises, then prays two units of prayer has the reward like that of Hajj and `Umrah.
Shaikh Ibn ul-Uthaymeen rahimahullah also graded it Hasan:
870 سئل فضيلة الشيخ: سمعت حديثاً وهو: “من صلى الفجر في جماعة، ثم جلس يذكر الله حتى تطلع الشمس، ثم صلى ركعتين، كانت له كأجر حجة وعمرة تامة، تامة، تامة” (1) ، السؤال: هل هذا الحديث صحيح أو ضعيف؟ وجزاكم الله خيراً.
فأجاب فضيلته بقوله: هذا الحديث له شاهد في صحيح مسلم (2) ، أن النبي صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ كان إذا صلى الفجر جلس في مصلاه حتى تطلع الشمس حسناً، لكن الذي في الصحيح ليس فيه ذكر أن الرسول صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ كان يصلي بعد ذلك، والحديث الذي ذكره السائل لا بأس به، إسناده حسن.
Whoever prays Fajr in congregation, then sits remembering Allah until the sun has risen, then he prays two Rak’ah, then for him is the reward like that of a Hajj and Umrah.” He said: “The Messenger of Allah said: ‘Complete, complete, complete.'” Question: is this Hadith Saheeh or Daif? Jazakallahu Khairan
This Hadith has a witness in Saheeh Muslim that the Prophet sallahu alayhi wa salam, if he prayed fajr, sat in his prayer place until the sun rose well. However, the narration in the Saheeh does not mention that the Messenger sallahu alayhi wa salam used pray after that. The Hadith mentioned by the questioner has nothing wrong with it and its chain is Hasan”
[Majmoo’ Fatawaa (14/299) no. 870]
And Allah knows Best
Translated and compiled by
Faisal Ibn Abdul Qaadir Ibn Hassan