Is it permissible to abbreviate (swt) for subhanhu wa ta’aala and is it permissible to abbreviate (saw) for sallallahu alayhi wasallam ?
Imam al-Nawawi, the great muhaddith and Shafiee faqih (Allah have mercy on him) states in his introduction to the commentary of Sahih Muslim
It is praiseworthy (mustahab) for a person writing Hadith that at the mentioning of the Messenger of Allah (Allah bless him & give him peace), he writes “Sallallahu Alayhi Wasallam” in full and not merely using abbreviations, and neither sufficing on one of the two, i.e. Salat Salam. (Sharh Sahih Muslim, 1/39)
Shaykh Yahya Al-Hajooree was asked:
What is the ruling on that which has spread among many of the Muslims from shortening the prayer upon the prophet, may the peace and blessings of Allah be upon him and his family and contentment with just the letter [s]?
This is a mistake and is insufficient, and opposite to what is correct. For that which is correct is that you write the phrase [may the peace and blessings of Allah be upon him and his family] and if you want you can write [may the peace and blessings of Allah be upon him] because both of these wordings are found. As for its abbreviation and contentment with the letter [s] or [saws] then this is a mistake.
This symbolic reference removes from you the reward of the prayer upon the prophet, may the peace and blessings of Allah be upon him and his family, and it denies from you the prayer of Allah in the most highest gathering, he said may the peace and blessings of Allah be upon him and his family: “he who sends prayers upon me once, Allah sends prayers upon him ten times” (Related by Muslim, Ahmed, Abu Dawood, At-Tirmidhee and Ibn Maajah on the authority of Abu Hurairah)