Firstly, it is noteworthy to state that the month of Ramadan is a blessed month and an opportunity for every Muslim to draw near to Allah, to increase his or her morality and spirituality, and to gain abundant rewards. Tarawih prayer is one of the very special characteristics of this month.
In responding to this type of mistake or situation whereby the Imam forgets to make Salam until the third rak’ah, and after which he brings one rak’ah to make the four rak’ah and them makes salam, the eminent Muslim scholar and renowned Da`iyah, Sheikh `Abdel Khaliq Hasan Ash-Shareef, states:
“Tarawih prayer in that case is valid and the Imam is not in need to repeat the prayer again. Although it is one of the Sunnans of the Prophet (peace and blessings of Allah be upon him) to observe nawafil in two separate rak’ah“.
May Allah accept our fasting and guide us to the straight path Amen.