In case the Imam forgets and offers an additional Rak`ah in a supererogatory Salah
Q 1: Last Ramadan, I offered the Tarawih (special supererogatory night Prayer in Ramadan) in congregation in the large Masjid (mosque) in our village. Our village judge led us in the ‘Isha’ (Night) Prayer, then a scholar - a kind man who has memorized the Qur’an and works as a teacher in the academic institute in our village - took over and led us in the Tarawih Prayer.
(Part No. 6; Page No. 27
If the reality is as you mentioned, then the Salah is valid.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.