—most of the time.
As for the report of Abū Hurayrah in which the Prophet, peace and blessings be upon him, is said to have commanded that whoever has prayed the two rakʿahs of Fajr should then recline on his right side: although al-Tirmidhī and Abū Dāwūd narrated it, and although the compiler here maintains that its chains are sound, the erudite scholar of the ummah and ocean of both rational and transmitted knowledge, Shaykh al-Islām Ibn Taymiyyah, judged the ḥadīth to be munkar (spurious). He affirmed that no authentic command to that effect can be traced back to the Prophet ﷺ—and this is indeed the correct verdict, for the Messenger never instructed anyone who had prayed the Sunnah of Fajr to lie on his right flank.
The author’s note in the chapter heading, “There is no difference between one who engaged in night vigil and one who did not,” points to the scholarly disagreement on the matter. Some jurists hold that reclining after the two rakʿahs of Fajr is recommended in every case; others say it is not recommended at all; and a third group distinguishes: if a person performed tahajjud (late-night prayer), it is recommended that he recline afterward to rest from the exertion, but if he did not pray at night, he should not recline.
Among the most astonishing and unusual opinions is the claim by some scholars that reclining after the Sunnah of Fajr is a condition for the validity of the Fajr prayer itself, so that whoever omits it, his prayer is invalid. Such statements are curiosities of learning. What connection could there possibly be between this reclining and the Fajr prayer? The two matters are entirely separate; the prayer has nothing at all to do with lying down. I have mentioned this only so that you may appreciate how some opinions—may Allah pardon their proponents—lack support from either revelation or sound reason.
The correct view is that of Shaykh al-Islām: if a person is weary from his night vigil, he may take a rest.