Is it obligatory to repeat the prayer after forgetting to complete the recitation of Al-Fatiha before bowing with the Imam, and completing it during bowing?

Al-Fatihah is a pillar of prayer for the Imam, the congregant (ma'mum), and the individual praying alone, in every rak'ah, except for the latecomer (masbuq) if he catches the Imam bowing or standing and is unable to recite it. Scholars have differed regarding its omission for the congregant if he forgets to recite it. Some are of the view that it is not dropped due to forgetfulness, while others hold that it is dropped for him, and this latter opinion is the more preferred one, especially concerning the congregant. Based on this, your prayer is valid. Completing Al-Fatihah during bowing, and your saying of takbir and tasbih, does not invalidate the prayer. However, recitation's proper place is during standing. Your prayer is valid according to the opinion that Al-Fatihah is dropped for the one who forgets. This does not harm you; rather, the prostration of forgetfulness (sujud as-sahw) is recommended. However, there is no prostration of forgetfulness required of you if you were a congregant from the beginning of the prayer.