Is the rakʿah in which the worshiper caught the imam bowing, after the latter had sat for the Tashahhud mistakenly, considered valid, or is he required to repeat it after the imam's salām?

If the latecomer stands up straight then bows without reciting Al-Fatihah, his prayer is valid and the Imam bears the responsibility of Al-Fatihah for him. However, if he moves directly from sitting to bowing, that raka'ah is not counted, and he must perform another one.