“Indeed, those who are closest to Allah are the ones who begin the salām.” Narrated by Abū Dāwūd with a sound chain.

Al-Tirmidhī also transmitted it from Abū Umāmah (may Allah be pleased with him). Someone asked, “Messenger of Allah, when two men meet, which of them should start the salām?” He replied, “The one who has the stronger claim to Allah, Most High.” Al-Tirmidhī said: a good ḥadīth.

134 – Chapter: Recommending that the salām be repeated
for a person one meets again within a short interval—
such as entering and then exiting and immediately re-entering, or when a tree or the like comes between them.

864 – Abū Hurayrah (may Allah be pleased with him) related—in the story of the man who prayed poorly—that the man came and prayed, then approached the Prophet ﷺ and offered salām. The Prophet returned the greeting and said, “Go back and pray, for you have not prayed.” The man went back and prayed, then returned and greeted the Prophet again; this occurred three times. Agreed upon.

865 – From the same Companion, the Messenger of Allah ﷺ said: “When one of you meets his brother, let him greet him with salām; and if a tree, wall, or stone comes between them, then he meets him again, let him greet him with salām once more.” Narrated by Abū Dāwūd (1).

135 – Chapter: Recommending the salām when one enters his own house
Allah the Exalted says, “So when you enter houses, greet one another with a salutation from Allah, blessed and good” ⦗24:61⦘.