Is the action of the worshiper who added a fifth raka'ah and performed the prostration of forgetfulness (sujud al-sahw) correct, after reciting the tashahhud instead of Al-Fatiha in the fourth raka'ah?

Al-Fatihah is a pillar of prayer. Therefore, whoever omits it forgetfully and remembers during the Tashahhud, must perform an additional rak'ah after the Imam's salutation, to compensate for the invalid rak'ah. He is not required to perform the prostration of forgetfulness (sujood as-sahw) because the Imam bears it on his behalf. However, his prayer is not invalidated by the additional prostration of forgetfulness.