How did the Prophet Muhammad, may Allah's peace and blessings be upon him, give and receive greetings of peace, and was it reported from him that he returned the greeting with the addition of "and His forgiveness"?

For a Muslim, it is permissible to limit the salutation of peace to "As-salamu alaykum" (Peace be upon you). However, it is better to add "wa rahmatullah" (and the mercy of Allah) or "wa barakatuh" (and His blessings). As for the one greeted, they should respond in kind or exceed it, based on Allah's saying: "And when you are greeted with a greeting, greet in return with one better than it, or (at least) return it." (An-Nisa: 86). The hadiths indicate that the most complete form for initiating the greeting is "As-salamu alaykum wa rahmatullahi wa barakatuh" (Peace be upon you, and the mercy of Allah, and His blessings), and for responding, it is "Wa alaykum as-salamu wa rahmatullahi wa barakatuh" (And upon you be peace, and the mercy of Allah, and His blessings). Every addition is considered good deeds. However, the addition of "wa maghfiratuh" (and His forgiveness) has not been authentically established in sound hadiths.