Is it obligatory to make the Adhan, or should Fajr prayer be performed immediately if a worshipper enters the mosque after the Adhan has concluded in other mosques and other worshippers have already entered?

It is sunnah to make the adhan upon entering the mosque if the adhan has not been made there for the prayer, even if other mosques have made it. It is a sunnah for a group that seeks others for prayer in every mosque or place where people habitually gather, and for an individual. The adhan should preferably be made at the beginning of the prayer time, and it is permissible at any time as long as the prayer time remains. It is also permissible to repeat it. The adhan is a communal obligation (fard kifayah) upon the entire neighborhood as one of the rituals of Islam. Whoever performs it has done the sunnah, and whoever leaves it has left the sunnah. It should not be left except due to lack of time. The adhan is legislated even if the congregation overslept and missed the prayer until sunrise.