What is prescribed is to write “salla Allaahu ‘alayhi wa salaam (May Allaah send blessings and peace upon him)” in full, and not to write it in abbreviated form, such as writing (S) or (SAWS) etc.
Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) said:
As it is prescribed to send blessings upon the Prophet (peace and blessings of Allaah be upon him) in prayer when saying the tashahhud, and it is prescribed when giving khutbahs, 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 Allaah 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 Allaah 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 Allaah in His Book, where He says (interpretation of the meaning):
“Send your Salaah on (ask Allaah to bless) him (Muhammad), and (you should) greet (salute) him with the Islamic way of greeting (salutation, i.e. As‑Salaamu ‘Alaykum)”