Is the prayer valid for the latecomer who joined the Imam after the Imam had given the salutation to the right, performed the prostrations of forgetfulness (sujood as-sahw), and sat for the tashahhud, then the worshipper stood to complete his prayer, or is it obligatory for him to repeat the prayer?

It is better for one to repeat the prayer if he did not catch the congregational prayer, as his prayer does not become valid by joining the Imam after the Imam’s first Taslim (salutation of peace), as mentioned by Shaykh Ibn Uthaymin. When the Imam performs the first Taslim, he begins to exit the prayer.

As for catching the congregational prayer, it is by joining the Imam before the prostration of forgetfulness (sujud al-sahw) if the Imam has given the first Taslim, as stated in Al-Insaf by Al-Mardawi. An exception to this is if one pronounced the takbir assuming the Imam had not yet given the Taslim, but then it became clear to him that the Imam had already given it, and then the Imam returned for the prostration of forgetfulness; in this case, his prayer is valid, as stated in the commentary by Al-Bujayrimi.