Assalaamu 'alay kum,
Where does the imam turn after the prayer, toward the people facing them directly or toward his right or left? Or are all three of these three places reported from the sunnah?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

According to the Sunnah, the Imaam is to face the people being led in the prayer after reciting Tasleem, and there is nothing wrong with him turning to his right or to his left (to face them), for both actions were authentically attributed to the Prophet .

Ibn Al-Qayyim said in Zaad Al-Ma‘aad about the guidance of the Prophet, sallallaahu ‘alayhi wa sallam, after reciting Tasleem in the obligatory prayers: “After reciting Tasleem, he used to seek forgiveness thrice and then say, ‘Allahumma Anta As-Salaam wa minka As-Salaam, Tabaarakta ya Thal-Jalaali wal-Ikraam (which means: O Allah, You are As-Salaam [the One Who is free from all imperfections] and from You is all peace, blessed are You, O Possessor of majesty and honor.)’

He would remain facing the Qiblah only for the length of saying that, then he would turn right away to face the people whom he had led in prayer.

He would turn to his right or to his left. Ibn Mas‘ood said: ‘I saw the Messenger of Allah turn to his left often.’

Anas said: ‘I saw the Prophet turn to his right often.’ The first Hadeeth was narrated by Al-Bukhaari and Muslim, and the second was narrated by Muslim.

‘Abdullah ibn ‘Amr said: ‘I saw the Messenger of Allah turn right (sometimes) and turn left (sometimes).’ He added: ‘He used to face the people that he led in prayer without facing one side of them apart from another.” [End of quote]

Allah Knows best.