Is the Imam's prayer valid if he did not sit for the middle Tashahhud and completed his prayer and prostrated for forgetfulness (sujud al-sahw), while the congregants behind him did not complete it, and should the congregants have completed the prayer with him no matter what mistake he made?

If the Imam forgets the first tashahhud and remembers it before standing fully upright, he should sit for the tashahhud and perform the prostration of forgetfulness (sujood as-sahw) if his return was closer to the sitting position. However, if he has already stood up fully, he should not return for the tashahhud but rather continue his prayer and perform the prostration of forgetfulness before the taslim, based on the hadith of Ibn Buhaynah. If he intentionally and knowingly returns after having stood up fully, scholars have differed regarding the invalidity of his prayer, but the more preponderant view is that it becomes invalid. The Imam's first prayer is valid, while for the congregants, it was obligatory to follow the Imam. If they did not follow him due to ignorance and then repeated the prayer, their second prayer is valid.