Is it permissible to repeat the prayer in this situation, after catching one rak'ah with the Imam in the first mosque, then repeating the prayer in another mosque to catch the congregation again?

Scholars have differed regarding the permissibility of repeating the Fajr prayer in another mosque to attain the virtue of congregational prayer. Some have prohibited it, arguing that performing supererogatory prayers after the Fajr prayer is forbidden until the sun rises. The Hanbalis are of the view that it is recommended to repeat the congregational prayer only for those who were already inside the mosque, and it is not permissible to repeat it during the prohibited time for those who were outside. As for the Shafi'is, they consider it permissible to repeat the prayer to achieve the virtue of congregation, even during the prohibited time, and even for those who already prayed it in congregation.