ASSALAMUALAIKUM.
May I know the ruling for allowing Non-Muslim to use the word ALLAH to call their God, e.g : Christian, Jews, Buddha, etc.
Wassalam.

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

Giving the name “Allaah” to a creature or an idol is blaspheming Allaah’s Names. As far as we know, the non-Muslims did not participate with the Muslims in using this great Name “Allaah” rather, it is only the Muslims who use it to refer to the True God, the One, and Only One, the Self-Sufficient Master.

As regards the issue of whether or not the Muslims may forbid the non-Muslims of other religions from using this Name to refer to their gods, then in principle, they are left to what they worship but if it is necessary not to allow them to use it due to the fear of harm or temptation that may cause to the Muslims, or for other reasons, then in this case the Ahl-ul-Hall wal 'Aqd (the decision makers and the influential members of the Muslim society), the scholars and jurists should gather in order to study the case (and take an appropriate decision).

Allaah Knows best.