The Ruling on the Prayer of One Who Greeted After the First Sitting by Mistake

Question
A person prayed the obligatory Dhuhr prayer, and in the first sitting after the testimony, he greeted mistakenly. Does he have to repeat the prayer, or does he build on it with two additional units? And how does he build?
Answer
I say, and with God's success: he builds on it two rak'ahs as if he had not exited, then he prostrates for forgetfulness and then he gives the salutation, and God knows best.
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