Is the Tarawih prayer valid if led by an Imam who completed it in four rak'ahs and performed the prostration of forgetfulness (sujud al-sahw), after he thought in the second rak'ah that it was the first, then remembered this in the following rak'ah and did not sit?

The Imam was obligated to return [to the correct number of rak'ahs] immediately upon recalling the excess in the Tarawih prayer, even if he recalled it at the end of the third rak'ah. He should perform the prostration of forgetfulness (sujud (definition) al-sahw) after the salām, because it was an addition. If he did not return intentionally, his prayer is invalidated because the night prayer is "two by two." However, if he was unaware of the ruling, then his prayer is valid as an absolute supererogatory prayer according to the Shafi'i school.