The hadith indicates that lying down after the two rak‘ahs of Fajr is prescribed. It also appears to indicate that doing so is obligatory, since that is what the command entails. (1) However, the following hadith provides grounds for construing the command as a recommendation rather than an obligation:
B) Aisha reported: “After the Prophet—peace and blessings be upon him—performed the regular sunnah prayer of Fajr, he would converse with me if I was awake; otherwise, he would lie down until the call to prayer was made.” Narrated by al-Bukhārī. (2)
This hadith shows that the Messenger—peace and blessings be upon him—would sometimes refrain from lying on his right side after the regular sunnah prayer of Fajr. Had it been obligatory, he would not have omitted it.
Claims that this was exclusive to him, or any similar claims, cannot be established without evidence. The presumption is that it applies generally, and acting upon everything reported from him—peace and blessings be upon him—is preferable to acting upon some reports to the exclusion of others.
The hadith indicates that lying on one’s right side is prescribed.
Should this be done at home or in the mosque?
The hadith of Abu Hurayra is unrestricted: if a person performs the regular sunnah prayer of Fajr in the mosque, he should lie down in the mosque; and if he performs it at home, he should lie down at home. However, it has not been reported that