Is it permissible for someone who has prayed Fajr to change the place where they prayed and sit remembering Allah, or must they remain in their spot?

It is understood from the noble hadith (definition), "Whoever prays Fajr in congregation, then sits remembering Allah until the sun rises, then prays two rak'ahs, will have a reward like that of a complete, complete, complete Hajj and Umrah (definition)," that this reward does not require the worshiper to remain in the exact spot of his prayer. Rather, it suffices for him to remain in the mosque remembering Allah the Almighty. So, if he moves within the mosque and sits remembering Allah, the hadith includes him. Some scholars have held that what is meant by "his prayer place" is the entire mosque, citing the hadith of Jabir ibn Samurah that the Prophet, peace and blessings be upon him, used to sit in his prayer place after Fajr until the sun rose, and he would turn to his companions and converse with them. This indicates that what is meant by sitting is remaining in the mosque, not in the exact spot where he prayed.