Reciting al-Fatihah in prayer is obligatory for the imam, the one who is praying alone and the one who is praying behind an imam, in prayers where Qur'an is recited silently and those where it is recited out loud, because of the general meaning of the evidence about reciting al-Faatihah in the prayer.
If a person catches up with the imam when he is bowing – the rak’ah in which he caught up with the imam bowing counts for him, according to the more correct of the two scholarly opinions, and the obligation to recite al-Faatihah is waived for him, because he is not able to recite it. That is based on the well-known hadeeth of Abu Bakrah al-Thaqafy, may Allah be pleased with him, who said that he came to the Prophet (peace and blessings of Allah be upon him) when he was bowing and he bowed before he reached the row. He mentioned that to the Prophet (peace and blessings of Allah be upon him) and he said: “May Allah make you more keen, but do not do it again.” Narrated by al-Bukhaari, 783
The Prophet did not ask him to make up for the rak'ah, this proves that al-Fatiha is waived if the person did not catch up bowing with the Imam.
"The meaning of the hadith is that may Allah make you keener to do good deeds, but do not bow before reaching the row because it is a disliked act."