Is it permissible to take a congregant as an Imam?

It is not permissible for a follower to be an Imam at the same time, because it is impossible for one to be both a follower and a leader. As for the latecomer who stands up to complete what he missed, it is permissible for others to follow him and make him an Imam according to a group of scholars, especially if he did not catch one or more complete cycles (rak'ah) with the Imam. Similarly, a follower may become an Imam if an impediment occurs to the Imam, and he is designated as his successor.