The Imam's Prostration for Forgetfulness After Reminding the Worshippers

Question
A group prayed the Dhuhr prayer in congregation, and then in the fourth rak'ah, they prostrated three times instead of two. After the tasleem, one of the worshippers reminded the Imam of the mistake, so the Imam immediately prostrated for forgetfulness. Is the prayer valid?
Answer
I say, and with God's help: If the imam prostrates before speaking or turning away from the qibla, his prostration is valid, as is that of those who are following him, provided they do not speak or move away from the direction of the qibla; otherwise, it is not valid. And God knows best.
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