All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the mentioned Imaam had repeated Al-Faatihah along with some other verses out of forgetfulness, then it is legislated for him to make Sujood as-Sahw (prostration for forgetfulness).
Ad-Dusooqi (from the Maaliki school) said in his book, Al-Haashiyah: “If the verbal element of the prayer was an obligation, like (the recitation of) Al-Faatihah, then he (the Imaam) should make Sujood as-Sahw for repeating it, if he was certain about repeating it and it was done out of forgetfulness, or, if even he was unsure about it, according to the opinion of some of the scholars (of the Maaliki School).”
Besides, Ibn Hajar Al-Haytami (from the Shaafi'i school) was asked as per his book, Al-Fataawa Al-Fiqhiyyah Al-Kubra: “If one repeats Al-Faatihah twice, is it a Sunnah for him to prostrate for forgetfulness?" He answered (within a long answer): “…He is to prostrate for forgetfulness for repeating Al-Faatihah as Az-Zarkashi quoted Ar-Raafi’i as saying. This is a reasonable opinion even though some later scholars decisively asserted otherwise.”
However, the prayer is not invalid and it is not an obligation to repeat it because of leaving Sujood as-Sahw here. Al-Buhooti (from the Hanbali school) said in his book, Ar-Rawdh: “The prayer is not invalid because of deliberately leaving out a prostration that is a Sunnah [i.e. not an obligation].”
The strongest opinion is that it is better to perform Sujood as-Sahw, in the case in question, after Tasleem, because it is due to an addition in prayer; this is the view of Imaam Maalik and the chosen opinion of Ibn Taymiyyah . Also, Sujood as-Sahw that is performed after Tasleem can be done even after a long time (from having finished the prayer). Therefore, the people who were praying behind the Imaam could do it whenever they want to even if the Imaam did not do it.
For more benefit, please refer to Fataawa 81875 and 86560.
Allaah Knows best.