Is the prayer of a man who entered the mosque after Asr, prayed two rak'ahs, then saluted and became a follower behind another person, then stood to complete the two rak'ahs after the Imam finished his prayer, valid?

It is permissible for someone praying a supererogatory prayer to be led in a congregational obligatory prayer, according to some scholars. After the first person finishes their supererogatory prayer, they can then join the second person for the remaining two rak'ahs of their obligatory prayer, and then make up what they missed.