Answered by Shaykh Faraz Rabbani
I have observed some brothers praying the two Sunnah rakats of Salatul Fajr immediately after the Fard rakats are prayed (i.e. when they are running late or the jamat is in progress when they arrive). From my knowledge of the Hanafi maddhab, I understand that the two Sunnah are only to be missed in the case where praying them may lead to missing the jamat, and in that case the earliest possible time to pray them is after sunrise since the time between Fajr salah and the end of sunrise is makruh for prayer. I am very keen on advising them of this point, but since they may follow a different school of thought, I am reluctant in case I may offend them. Please advise me on this point. Is there any evidence to support the praying of the Sunnah rakats after the fard rakats in any maddhab if they are missed before the fard?
What they do is the recommended course of action in the Shafi`i school. If they are non-Hanafis, leave them alone. If Hanafi, give them nasiha (advice), if you think they would listen.
In the Hanafi school, it would be prohibitively disliked (and sinful) to pray the sunnas of fajr after praying the fard of fajr.