Polite reminder that Christians whose first language is Arabic do in fact pray to Allah, by which they mean the God of Abraham and the Father of Jesus.
Allah means God in Arabic, in the same sense that Dios means God in Spanish and Deus means God in Latin.
Do not confuse the name with the Being, and do not allow those who profit from the confusion to prosper.
https://christiananswers.net/q-eden/allah.html
Both Lumen Gentium and JP II's catechism specify "muslims".
And I challenge you to ask any muslim if he worships the same "allah" that Christians worship.
It's embarrassing to see the Catholic Church telling muslims that which they don't believe themselves.
Allah does not mean “god”; it is a proper name of an old Arab pagan moon god, who had a female counterpart named Allat. The name is not cognate with Hebrew “Eloah”. Those who claim that it is a contraction of Arabic “al-ilah” are not telling the truth.
None of the characteristics of Mahomet’s Allah match that of the God of Abraham, Isaac and Jacob. For one of the most explicit examples, Allah explicitly states in several Koranic verses that he has not “taken unto himself a son” (e.g. Surah 2:116, 10:68, 19:35). Surah 11:42 claims that Noah lost one of his (unnamed) sons to the Great Flood, while the Bible says that God saved Noah’s entire family. This can go on and on.