255 – Waʾil ibn Ḥujr (may Allah be pleased with him) said: “I prayed behind the Prophet ﷺ. When he finished, he would give the salām to his right, saying, ‘as-salāmu ʿalaykum wa raḥmatullāhi wa barakātuh (peace be upon you, and the mercy of Allah, and His blessings),’ and to his left, ‘as-salāmu ʿalaykum wa raḥmatullāh [wa barakātuh].’” Reported by Abū Dāwūd with an authentic chain (1).

— Degree of authenticity —
This hadith is sound. Abū Dāwūd transmitted it with a reliable chain, and it was declared authentic by ʿAbd al-Ḥaqq, al-Nawawī, and Ibn Ḥajar; all its narrators are trustworthy, several of them belonging to the transmitters of the two Ṣaḥīḥ collections.

Al-Albānī said: “It is preferable not to make a habit of adding wa barakātuh, since that wording is not found in the other narrations of the salām.”

Shaykh al-Mubārakfūrī commented: “Know that most manuscripts of Sunan Abī Dāwūd omit the addition wa barakātuh in the second salutation and record it only in the first, so much so that some people supposed al-Ḥāfiẓ Ibn Ḥajar erred by citing it with the second. In fact, the mistake lies with those critics, for this extra phrase with both salutations is present in a number of sound, authoritative manuscripts.”

— Points derived from the hadith —
1 – In legal terms, prayer is defined by the scholars as specific words and actions that begin with the takbīr and conclude with the taslīm. The Prophet ﷺ said, “Its release is the taslīm.” [Reported by Aḥmad (1009)].

2 – The wording of the taslīm is: “as-salāmu ʿalaykum wa raḥmatullāh” said twice, once to the right,