MAY ALLAH HONOUR HIM AND GRANT HIM PEACE
May Allah honor Him and grant Him peace (In Arabic: Sallal laahu alaihi wa sallam) is a statement which sends the supplications of Peace on Prophet Muhammad (May Allah honor Him and grant Him Peace). It’s a kind of supplication.
Arabic - صلى الله عليه وسلم(or)ﷺ
Allah سبحانه و تعالى sends down His blessings on the Prophet ﷺand His angels pray for him. O you who believe, you too should invoke His blessings on him and salute him with the salutation of peace. : Qur’an.SurahAzhab 33:56. 
"The Messenger of Allah ﷺ said, May he be humiliated, the man in whose presence I am mentioned and he does not send Salah upon me; may he be humiliated, the man who sees the month of Ramadan come and go, and he is not forgiven; may he be humiliated, the man whose parents live to old age and they do not cause him to be granted admittance to Paradise." Fiqh Us Sunnah 4.138 and Tirmidhi , Tuhfat al Ahwadhi 9:531 
"The Messenger of Allah ﷺsaid: Whoever sends one salah upon me, Allah will send ten upon him." Sahih Al Muslim 747.
It is the practice of the Sahaba (Male and Female Companions of Prophet Muhammad (May Allah honour Him and grant Him peace))to send the blessings on Prophet Muhammad (May Allah honor Him and grant Him peace) in full. No Sahaba has used any short form of greeting like: SAW, PBUH, etc.