Is it permissible to make up the Sunnah (recommended prayers) of Fajr after the obligatory Fajr prayer?
Chapter on the Times When Prayer is Prohibited
Al-Mughni
Book of Prayer
Primary text
Making up the two Rak'ahs of the Sunnah of Fajr after the obligatory Fajr prayer is permissible. Al-Shafi'i, 'Ata', and Ibn Jurayh permit it based on the report of Qays ibn Fahd, who stated that the Messenger of Allah (peace be upon him) saw him praying the two Rak'ahs of Fajr after the obligatory prayer and did not forbid it when informed of the reason. The silence of the Prophet (peace be upon him) indicates permissibility. Furthermore, the Prophet (peace be upon him) made up the Sunnah of Dhuhr after Asr, and the Sunnah of Fajr is analogous to it. It is also likened to the two Rak'ahs of Tawaf because it is a prayer associated with a specific reason (Sabab).
Supporting text
Imam Ahmad preferred making up these two Rak'ahs during Duha time (mid-morning), although he stated that praying them after Fajr suffices. Ibn 'Umar used to make them up during Duha. The stance of the Ahl al-Ra'y (Hanafi school) is that it is not permissible due to the generality of the prohibition found in traditions, such as the narration from Abu Hurayrah stating that whoever misses the two Rak'ahs of Fajr should pray them after sunrise.