What is the ruling on the prayer of someone who caught the last Tashahhud with the Imam, completed the Tashahhud and the supplication thereafter, then stood up for the missed rak'ah after the Imam had given the Tasleem?

If you join the Imam in the last tashahhud and he gives the salutation, you must stand up immediately and not prolong your sitting to complete the tashahhud, because this is not the place for you to recite the tashahhud. If you deliberately sit after the Imam's salutation in a place that is not the usual tashahhud position, your prayer becomes invalid. However, if that position is where your first tashahhud would have been, it is permissible to sit, but it is disliked (makruh). If you do not stand up immediately when it is not your tashahhud position, your prayer becomes invalid if you did so intentionally. If you did so out of forgetfulness, you must perform the prostrations of forgetfulness (sujud al-sahw).