1) My question is: recently I have noticed a trend that many people in the email and chats, use abbreviation for Islamic greeting (for e.g.: W/S for Wa Alaikum Assalaam, ASAK for Assalaam Alaikum, AH for Allah Hafiz) and the like. I was wondering if this is a good practice and should it be encouraged. Please clarify my confusion.
Another question I have is linked with the first question which was posed by a friend.
2) Why do Islamic scholars in particular and the rest in general use the abbreviation [(PBUH), Allah (swt) and the like] when addressing Allah (The Almighty) Himself or the Prophet of Allah (peace be upon him)? What is the justification/explanation for it?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Using abbreviations of sending blessing upon the Prophet instead of the complete expressions of invoking blessings upon the Prophet is not allowed as stated clearly by the former and contemporary scholars.

There are many benefits in invoking blessings upon the Prophet Muhammad :

a)  Obeying the Commandment of Allah, and imitating Allah and His angels as Allah Says (what means): {Indeed, Allah confers blessing upon the Prophet, and His angels [ask Him to do so]. O you who have believed, ask [Allah to confer] blessing upon him and ask [Allah to grant him] peace. (salutation i.e. As­Salâmu 'Alaikum).} [Quran 33:56]

b) Increasing the reward of the one who invokes blessings; hoping in having his supplications being answered; getting the blessings and keeping on the love of the Prophet ; achieving the guidance and giving life to the heart. The more one invokes blessings on the Prophet the more he increases his love and affection to him till he does not feel any resistance to the commands of the Prophet and his teachings in himself. Moreover, there are many Ahadeeth that urge Muslims to invoke blessings on the Prophet . Imam Muslim reported that the Prophet said: “Whoever invokes blessings on me once, Allah will bless him ten times."  The Prophet also said: "Do not turn you houses into graves, do not make my grave as a place of feast, and invoke blessings on me since your blessing reach me from wherever you are.” The Prophet also said: “May that person be humbled in whose presence my name is mentioned but he does not invoke blessings upon me.” [At-Tirmithi]

Invoking blessings upon the Prophet is legislated during prayers, Khutbah [Friday speech], supplications, Athaan, while entering the mosque, going out of the mosque, when the Prophet is mentioned and at other occasions. It becomes more emphatic to write the full expression of blessings when his name is mentioned in a book, letter, article, research work, etc, for the above pieces of evidence.

It is legislated to write the expressions of blessings completely following the Order of Allah and to remind the reader of the blessing. Thus, writing the abbreviation, such as (pbuh) should be avoided.

Imam Ibn as-Salah wrote in his book Uloom al-Hadeeth which is known by the name Muqaddimatu Ibn as-Salah: “One should keep on writing the words of blessing on the Prophet and should not get tired of repeating them whenever his name is written. This is one of the best benefits gained by those who study the Hadeeth and its sciences. Whoever neglects it fails to achieve these huge benefits. We have seen many good dreams about such people who used to repeat writing blessings on the Prophet . Writing blessings on the Prophet is a Du’a (supplication); hence one should write it while copying a Hadeeth or a book of Hadeeth, even if it is not found in the original text.”

The same ruling applies to the words of glorification that are written with the names of Allah, such as Azza wa Jalla, Tabaraka Wa ta’aala, etc.

For more benefit, please refer to Fataawa 246610 and 363448.

Allah knows best.