Is delaying prayer to perform it in congregation after a lesson better than performing it alone on time, and what are the proofs for the the obligation of congregational prayer in the mosque on time?

The first [priority] is that you pray in the mosque and then resume your lesson, if possible. However, you are not obligated to go to the mosque, as the majority opinion is that congregational prayer is not obligatory to be performed in the mosque; rather, its obligation is fulfilled by performing it anywhere. Nevertheless, you miss out on great virtue by witnessing the prayer in the mosques. And praying at the beginning of its time is better.