Is it essential to stay in the place where one prayed Fajr in order to obtain the benefit?
Question

If a person prays Fajr then moves from the place in which he prayed and sits remembering Allah, is that permissible or should he stay where he was in order to attain the reward?.
Praise be to Allah.Al-Tirmidhi narrated (485) that Anas (may Allah be pleased with him) said: the Messenger of Allah (blessings and peace of Allah be upon him) said: “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 Hajj and ‘Umrah, complete, complete, complete.” Classed as saheeh by al-Albani in al-Silsilah al-Saheehah, no. 3403. 
It seems that in order to attain this reward it is not essential for the worshipper to stay in the place where he prayed; so long as he is in the mosque, remembering Allah, may He be exalted, then there is the hope that he will attain this reward. This is indicated by the general meaning of the hadeeth: “Whoever prays Fajr in congregation then sits remembering Allah until the sun rises…” The Prophet (blessings and peace of Allah be upon him) did not stipulate that he should stay in the place where he prayed. So if he moves to another place inside the mosque, and sits remembering Allah, then the hadeeth includes him. This was stated by some of the scholars. Ibn Rajab (may Allah have mercy on him) said in Fath al-Baari (4/56): Several hadeeths have been narrated concerning the virtue of one who sits in the place where he prayed after Fajr until the sun rises and after ‘Asr until the sun sets. 
Is what is meant by the phrase “the place where he prayed” the spot where he prayed or the entire mosque in which he prayed? There is a difference of opinion concerning this. 
In Saheeh Muslim it is narrated from Jaabir ibn Samurah that the Prophet (blessings and peace of Allah be upon him), when he had prayed Fajr, would sit in the place where he prayed until the sun had fully risen. According to another report: the Prophet (blessings and peace of Allah be upon him) did not get up from the place in which he had prayed Fajr until the sun rose, then when the sun rose, he would get up. It is well known that he (blessings and peace of Allah be upon him) did not sit in the place where he had prayed, because he would go to his companions following the prayer and turn to face them. 
This was narrated by al-Tabaraani, who says: When he had prayed Fajr, he would sit and remember Allah until the sun rose. 
In the completion of the hadeeth of Jaabir ibn Samurah which was narrated by Muslim it says: And they would talk and discuss issues from the time of Jaahiliyyah and they would laugh and he would smile. 
This hadeeth indicates that what is meant by the place in which he had prayed and in which he would sit is the mosque as a whole. This was the view of a number of the scholars including Ibn Battah among our companions and others. End quote. 
And Allah knows best.