Is the prayer of the Imam and the congregants valid if the Imam prostrated once in the second رکعة, then the congregants alerted him, so he completed the prostration, then performed the prostration of forgetfulness (sujud al-sahw) after the tasleem, while some of the congregants did not perform the prostration of forgetfulness?

If the Imam prostrated the second prostration after being reminded, then recited the first tashahhud, prayed the third rak'ah, and performed two prostrations after the taslim, his prayer is valid. The prostrations of forgetfulness (sujood as-sahw) are prescribed for him based on the generality of the Prophet's (peace be upon him) saying: "For every forgetfulness, there are two prostrations after saying taslim."

The Imam here forgot and recited the tashahhud in the wrong place, which is an addition for which he prostrates after the taslim. The congregants who prostrated with him were correct in obeying the command of the Prophet (peace be upon him): "Indeed, the Imam was appointed to be followed." As for those who did not prostrate with him, they were mistaken for disobeying this command. Scholars unanimously agree on the obligation of following the Imam in the prostrations of forgetfulness.

As for the prayer of one who intentionally omitted the prostration, it is safer to repeat it, because some scholars consider the prayer invalid if the congregant intentionally fails to follow the Imam in the prostrations of forgetfulness. Others hold that the congregant's prayer is valid even if they fail to follow the Imam in the post-prayer prostrations. Al-Nawawi held that if the Imam prostrates in situations other than the two cases where the Imam's error is known, and the congregant intentionally fails to follow him, their prayer is invalidated.