The Catechism states that the Muslims worship the same God as we do.
841 The Church’s relationship with the Muslims. “The plan of salvation also includes those who acknowledge the Creator, in the first place amongst whom are the Muslims; these profess to hold the faith of Abraham, and together with us they adore the one, merciful God, mankind’s judge on the last day.”
Given that we believe God includes Jesus, then yes, Allah is the same God as Jesus.
It stands to reason if you believe in one God, then it’s the same God as our God. There is only one God, our God. If you choose to call him Allah, Yahweh, or George, it doesn’t matter. It’s the same God. No other gods exist.