Can the Sunrise Prayer be performed at home after the Dawn Prayer in the mosque?

Whoever prays Fajr in the mosque and sits remembering Allah until the sun rises, then prays two rak'ahs, will have the reward of a complete Hajj and 'Umrah. As for whoever goes home after the prayer and sits remembering Allah until the sun rises, they may pray two rak'ahs or more, and some scholars have mentioned that they also attain the reward mentioned in the hadith.