What is the ruling on one who did not hear the takbir of rising from prostration and did not attend the sitting with the Imam, then completed a rak'ah and prostrated for forgetfulness? And is what he did correct?

If the worshiper, when the Imam has concluded the prayer, makes up what he missed with the Imam, and then completes his prayer, and the Imam gives the salutation, and the worshiper stands for an additional rak'ah, then his prayer is invalid and must be repeated because he prayed five rak'ahs, when it would have sufficed him to give the salutation with the Imam.

However, if he did not make up what he missed with the Imam and followed him directly, then stood up after the Imam's salutation and performed an additional rak'ah, and performed the prostration of forgetfulness (sujood as-sahw), then his prayer is valid, and there is no blame on him, but the prostration of forgetfulness is not prescribed for him in this case.

The general rule is that the worshiper should make up what he missed and then follow the Imam if he does not fear missing the next rak'ah. But if he fears missing it, then he should follow the Imam, and his first rak'ah becomes void.