one extra rank for having reminded them of the salām; and if they fail to return his greeting, someone better than they will return it on his behalf.”
He added: “It was narrated by al-Bazzār and al-Ṭabarānī, and one of al-Bazzār’s two chains is sound and strong.”
There is also, on this issue, a report from Abū Hurayrah similar to Anas’s ḥadith. Al-ʿUqaylī recorded it, as cited in al-Jāmiʿ al-Kabīr (1/159/1).
In short, the ḥadith is unquestionably authentic. Numerous sound reports command the spreading of salām, some of them found in the Ṣaḥīḥ. I have chosen this particular ḥadith for discussion because, although it is not in the Ṣaḥīḥ, its chain is authentic and it has those corroborating narrations; I therefore wished to clarify that.
Once you realise this, you should know that the scope of the prescribed spreading of salām is very broad. Some people have narrowed it—either through ignorance of the Sunnah or negligence in acting upon it. One example is greeting with salām a person who is praying. Many assume this is not legislated; indeed, al-Nawawī explicitly deemed it disliked in al-Adhkār, even though in his commentary on Ṣaḥīḥ Muslim he stated that it is recommended to respond to the salām by gesture—and that is the Sunnah. Numerous ḥadiths relate that the Companions greeted the Prophet ﷺ while he was praying; he approved of their doing so and returned the greeting. I shall cite here just one of them—the report of Ibn ʿUmar, who said:
“The Messenger of Allah ﷺ went out to Qubāʾ to pray there. The Anṣār came to him and greeted him with salām while he was praying. I then said to Bilāl, ‘How did you see the Messenger of Allah ﷺ return the salām to them when they used to greet him while he was praying?’ He replied, ‘He would do like this,’ and he spread out his palm. Jaʿfar ibn ʿAwn likewise spread out his palm—turning its inner side downward and its back upward.”
185 — “The Messenger of Allah ﷺ went out to Qubāʾ to pray there. The Anṣār came to him and greeted him with salām while he was praying. Ibn ʿUmar said, ‘I then said to Bilāl, “How did you see…’”