Do Muslims really worship God?

As I understand, Muslims worship Allah, who is the same as the God of the Jews and the one God we worship. But the problem is, they don’t believe in Jesus as the Son of God or as part of the Holy Trinity, and just like the Jews, they have heard of Him yet they do not believe.
Jesus said He was “the way, the truth and the life” and no one goes to the Father except through Him. He also said to the Jews in John 3:18"Those who believe in the Son are not judged;but those who do not believe have already been judged, because they have not believed in God’s only Son."
To make it clearer, He also said to them,concerning the Father, in Jn 5:37-40"…You have never heard his voice or seen His face, and you do not keep His message in your hearts, for you do not believe in the one whom He sent. You study the scriptures, because you think that in them you will find eternal life."
Lastly,Jn 5:23"…Whoever does not honour the Son does not honour the Father who sent Him." These are very clear and unambiguous statements and from them (and more) I have concluded that they apply to Muslims as well as Jews. When Christ came the Muslims did not believe, they cling to the Koran and “think” they worship God, but in reality they don’t.
It is central to our faith to believe in Jesus’ divinity, and I have been a perplexed at a former Religious Education teacher of mine, at my former Catholic,Jesuit school, who claimed that Muslims worship the same God we do. In our faith, God is a union of three persons: Father, Son and Holy Spirit. Am I wrong about my conclusions? Thank you in advance.

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Recommended Reading:

*]Must I believe that Muslims worship my God?
*]Islamics - Hindus- Buddhists - saved without Christian Faith??
]If Allah is a name for God, what’s wrong with Catholics praying to him?
]John Paul II’s “Ecumenical Passion” A Clear-Eyed Look at Dominus Iesus b
y Msgr. John O. Barres

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