ABBREVIATING THE BLESSINGS SENT UPON THE PROPHET
What is prescribed is to write “صلى الله عليه وسلم[sulla Allahu alayhi wa-salam; peace and blessings of Allah be upon him]” in full, and not to write it in abbreviated form, such as writing (S), (SAWS), (PBUH), and the like.
Shaykh ’Abd al-’Azeez ibn Baaz (may Allah have mercy on him) said: As it is prescribed to send blessings upon the Prophet (peace and blessings of Allah be upon him) in prayer when saying the tashahhud, and it is prescribed when giving khutbah, saying du’aa’ and praying for forgiveness, and after the adhaan, and when entering and exiting the mosque, and when mentioning him in other circumstances, so it is more important to do so when writing his name in a book, letter, article and so on. So it is prescribed to write the blessing in full so as to fulfil the command that Allah has given to us, and so that the reader will remember to say the blessing when he reads it. So we should not write the blessing on the Prophet (peace and blessings of Allah be upon him) in short form such as writing (S) or (SAWS) etc., or other forms that some writers use, because that is going against the command of Allah in His Book, where He says (interpretation of the meaning):
“Send your salaah on (ask Allah to bless) him (Muhammad), and (you should) greet (salute) him with the Islamic way of greeting (salutation, i.e. A‑salaamu ’alaykum).” [al-Ahzaab 33:56]
And that (writing it in abbreviated form) does not serve that purpose and is devoid of the virtue of writing “salla Allahu ‘alayhi wa salaam (May Allah send blessings and peace upon him)” in full. Moreover the reader may not take notice of it and may not understand what is meant by it. It should also be noted that the symbol used for it is regarded as disapproved by the scholars, who warned against it.
Source: Islam QA
www.islamqa.info