Must I make up the prayer if I prostrated myself knowing that the Imam had already risen from prostration, and I did not subsequently perform the prostration of forgetfulness?

It is recommended for the latecomer to join the Imam in whatever position he finds him, whether bowing, prostrating, or sitting. The prayer is valid for someone who ignorantly adds an extra prostration of forgetfulness in the wrong place, and the Imam bears the forgetfulness of the worshipper as long as he is following him.