Yes, but The "Allah" of Islam is a false god originating from the pre-islamic arabian culture wherein there were 360 deities (sun, moon, stars). Allah was originally known as "Al-Ilah" and praying toward Mecca, pilgrimages to the Kabah, etc. were all in place before Mohammed. So much for the Koran coming directly from heaven to Mohammed. Islamic is an irrational cult that has no basis in evidence or archeology for the claims that it makes.
They call what they worship "God" (in their own language). "Allah" means "God" or if you prefer "god". Are they really worshipping God? I would say not. But that's what the word "Allah" means, cognate with the Hebrew "Eli".
Islam is patterned on a sort of twisted Judaism with a bit of twisted Christianity thrown in. The business of there being only one God didn't come from some pagan moon-cult, even if Islam still has some elements of it.