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

A: 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.