Fiqh-us-Sunnah Volume 4, Funerals and Dhikr, Fiqh 4.139.

The scholars hold it desirable to invoke Allah’s blessings upon the Prophet, peace be upon him, each time one writes his name. But this is not mentioned in any hadith, so none can be used to support this view. Al Khatib al-Baghdadi said, “I saw the handwriting of Imam Ahmad Ibn Hanbal and I found that often he wrote the name of the Prophet, peace be upon him, without invoking Allah’s blessings upon him.” Then he added, “It has come to my knowledge that he used to invoke Allah’s blessings upon the Prophet verbally.”

An-Nawawi said, “When invoking Allah’s blessings upon the Prophet, peace be upon him, we should combine prayers for peace and blessings upon him (by saying Salalahu ‘alaihi was sallam), and should not confine it to one of these saying either Sallahu ‘alaihi (May Allah shower His blessings upon him) or ‘Alaihi as-salaam (peace be upon him)’.”