Maybe I'm the one who is confused here. I thought that Hoss gave this quote from the catechism:
"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."
Then I saw that another poster said that proper interpretation of catechism (using context that would not be provided) does not lead us to think that Muslims worship the same God of the Holy Roman Catholic Church.
In your most recent post, you even say,
4. "We" includes the holy catholic apostolic church, the Jews, and those who profess faith in the God of Abraham (as do the Muslims), as having in common that all three profess to worship and adore the God of Abraham, Isaac, and Jacob. (emphasis mine)
I understand that Hagar thought she was serving the same God as Abraham but you #4 uses the present tense to claim equivalence.
I admit: it is hard for me to follow what is being said by you and the other poster, but plainly asked:
Does the Holy Roman Catholic Church believe that the God it worships is the same as the God who is worshiped by Muslims?
Please be patient with me. I am not playing "gotcha." That poster was wrong.
Jesus was the actual physical Creator so no the muzlims do not believe in the God of Creation...