In the Name of Allaah,the Most Gracious,the Most Merciful
Q: What is the ruling on sleeping after offering Fajr (Morning) prayer? Does it make the heart hard, and is it considered one of the evils?
A: There is no blame for sleeping after Fajr prayer, and I do not know of any prohibition concerning. The common belief among the people that sleeping after Fajr is not a good act and that is such and such, is baseless. Therefore there is no harm in sleeping after Fajr prayer. However, whoever sits in his Musalla (place for Prayer) after offering Fajr prayer to read the Qur’an, to seek forgiveness from Allah, to glorify Allah, to say Tahlil: ”None has the right to be worshipped except Allah”, or to say other invocations until the sun rises, then this will be better for him than sleeping. The Prophet (peace be upon him) used to do that, but whoever neglects doing so after Fajr prayer there is no blame on him. Therefore, it can be said that whoever leaves immediately after offering Fajr prayer for his needs, sleeps or to do other things, there is no blame on him.
Source: Fatwas of Nur ‘Ala Al-Darb, vol. 9|Book of Salah|alifta.net