What is the ruling on the prayer of one who, out of forgetfulness, bowed behind the Imam in a silent prayer before completing the recitation of Al-Fatiha?

If the congregant bows behind the Imam, having forgotten to recite Al-Fatiha in a silent prayer: if Al-Fatiha is a sunnah (recommended act), then there is nothing upon him, and he continues his prayer. However, if Al-Fatiha is wajib (obligatory), then the congregant follows the Imam, and then, after the Imam's salutation, he performs an additional rak'ah (unit of prayer) to compensate for the one in which he forgot Al-Fatiha. But if he remembers to recite it while standing in the second rak'ah, that rak'ah will be counted for him.