What is the ruling concerning an imam who does not say the salām to his right and left at the end of the prayer, claiming that the salām is only by utterance, and is the prayer of those behind him valid?

The turning of the worshipper's head to the right and left during the Taslim (salutation of peace at the end of prayer) is among the Sunan (plural of Sunnah, recommended acts) of prayer. The proof for this is the action of the Prophet, peace and blessings be upon him, as reported in the Hadith of 'Amir ibn Sa'd from his father. This is also what Al-Nawawi mentioned as being among the Sunan of prayer. Therefore, whoever omits turning their head, their prayer is valid, but they have forsaken a Prophetic Sunnah. The Prophet, peace and blessings be upon him, said: "Whoever turns away from my Sunnah is not of me."