An Imam forgetting the first Tashahhud and performing Sujud-ul-Sahw after completing the Salah, in spite of the Ma'mums drawing his attention through

A: Reciting the first Tashahhud is one of the obligatory actions in Salah. If the Imam forgets it and the Ma’mums draw his attention to it before he is standing fully erect, he is obligated to return and sit to recite the Tashahhud. But if he is already standing erect, then it is Makruh (disliked) for him to return and sit for the Tashahhud, even if the Ma’mums say, "Subhan Allah". If he is standing and has started to recite Surah Al-Fatihah, he is forbidden from going back to recite the first Tashahhud, because he has already started another Rukn (integral/Pillar) of the Salah, and he is obligated to recite Surah Al-Fatihah. (Part No. 6; Page No. 22) He is not permitted to leave a Rukn of Salah for an obligatory action, which can be compensated for by Sujud-ul-Sahw. Hence, what you did by concluding the Salah without returning to recite the first Tashahhud after fully standing up, and performing Sujud-ul-Sahw before the Taslim was correct. This is in accordance with the Hadith narrated by Al-Mughirah ibn Shu‘bah (may Allah be pleased with him) that the Messenger of Allah (peace be upon him) said: “If one of you is offering Salah and has stood up in place of sitting (for Tashahhud), if they have not stood up perfectly straight, let them sit (for Tashahhud), and they are not required to offer two prostrations (of forgetfulness); but if they have already stood up perfectly straight, let them continue their Salah and offer two prostrations (of forgetfulness) while sitting.” (Related by Abu Dawud, Ibn Majah, and Al-Daraqutny) Another evidence is the Hadith of `Abdullah ibn Buhaynah (may Allah be pleased with him) who narrated: “Once the Prophet (peace be upon him) led them in the Zhuhr (Noon) Prayer but he stood up after the first two Rak‘ahs without sitting down (to recite Tashahhud). The people stood up with him. When he (peace be upon him) finished the Salah and people waited for him to conclude it with Taslim, he said Takbir (saying: ‘Allahu Akbar [Allah is the Greatest]’) while sitting and prostrated twice before the Taslim and then he said the Taslim.” (Related by the Seven Compilers of Hadith [Al-Bukhari, Muslim, Abu Dawud, Al-Tirmidhy, Al-Nasa’y, Ibn Majah, and Ahmad]) (Part No. 6; Page No. 23) The wording is that of Al-Bukhari. May Allah give us success! May peace and blessings be upon our Prophet Muhammad, his family, and Companions!