Firstly: we have already stated in the answer to question no 10995 that reciting al-Faatihah is an essential part of the prayer without which the prayer is not valid. It is essential to recite it, whether one is praying alone, as an imam or behind an imam, and whether the prayer is one in which Qur’aan is recited out loud or quietly.
Secondly: If the imam forgets it in the first rak’ah, and he does not remember until he stands up for the second rak'ah, then the second rak’ah becomes the first rak'ah for him. Based on this, he has to offer another rak’ah to make up for the first rak’ah in which he did not recite al-Faatihah. With regard to the people praying behind him, they should not follow him in this rak’ah, rather they should sit for the tashahhud, then wait and say the salaam with the imam.
With regard to a person praying behind an imam who forgot to recite al-Faatihah, for those who say that the person who prays behind an imam does not have to recite al-Faatihah the matter is straightforward: he does not have to do anything. For those who say that it is an essential part of the prayer for him, and he is like the imam, then if he did not recite it, he has to offer another rak’ah after the imam says the salaam, unless he joined the prayer when the imam was bowing, or when the imam was standing but he bowed before he could finish reciting it. In that case he does not have to recite it in the first rak’ah.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) ، Liqaa’aat al-Baab il-Maftooh, 51.