All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Whoever finds the Imaam who leads the prayer in the position of Rukoo’ (bowing down) and bows down with him he can count that Rak'ah a valid one, and he is not obliged to repeat it. The evidence for this is the Hadeeth reported from Abu Hurayrah that the Prophet said: “If you come to the prayer while we are in the position of prostration (in prayer), you should prostrate with us but do not count it as a valid Rak'ah. And whoever catches up with us while in the position of Rukoo’, (i.e. before standing up from Rukoo’), he has caught up with the prayer.” [Ibn Hibbaan, Al-Mustadrak]
Thus, leaving the recitation of Soorah Al-Faatihah does not affect his prayer either because its recitation is not compulsory for the one who follows the Imam as it is the opinion of a group of scholars, or because the meaning of the Hadeeth which orders the recitation of Soorah Al-Faatihah is specified by the Hadeeth which is mentioned above.
However, the majority of the Muslim scholars are of the view that the Rak'ah is valid, so it can be counted by the one who catches up with the Imam in the position of Rukoo’.
Other scholars are of the view that if one catches up with Rukoo’, he has not performed a valid Rak'ah, and has then to repeat it. The basis for their viewpoint is that the recitation of Soorah Al-Faatihah is compulsory for both the Imam and the one who is led in prayer. But this viewpoint is weak.
Allah knows best.