Is it permissible to repeat the Fajr prayer for the sake of congregational prayer, or would I be mistaken due to the prohibition of praying after Fajr?

Repeating the prayer with a colleague to attain the virtue of congregational prayer is a مطلوب (desirable/required) act, and it does not contradict the prohibition of praying after the Fajr prayer. This is because the prohibition applies to prayers without a سبب (reason/cause), whereas prayers with a reason are not مكروهة (disliked/reprehensible). The second prayer is considered a نافلة (supererogatory prayer).