Do Muslims worship Abrahams God?

NO, FOR IF THE DID, THEY WOULD KNOW JESUS IS THE SON OF GOD AND GOD THE SON, WHICH THEY DENY.

THE GOD OF ABRAHAM SAID, >>>

"THIS IS MY BELOVED SON, IN WHOM I AM WELL PLEASED"

THY DO NOT TAKE UP OR LISTEN TO THE HOLY BIBLE WHICH IS THE ONLY TRUE WORD OF GOD, FOR THE WORD BECAME FLESH(JESUS THE CHRIST) AND DWELT AMONG US.

We worship only Allah

Yes , That is why Muslims raise Abraham as being the fore father of the last generation of mankind. Since he was the father of Ishmael and Isaac, Arab and Israel respectively.

There is only One God.  He is Triune and Jesus is His only Son.

Some seem to think so, but probably not.

There's only one God, His proper name is Allah anyone who says they worship God is worshipping either Allah or a false god. 

Thats probably why they are not unitied  as are Jehovahs Witnesses who although speaking 1000 languages in 240 lands all unitedly worship Jehovah God as Jesus His Son  instructed them and the Pharisees how to Math 22;37  Allah is not Gods name it is a title When Moses went to deliver the Israeliites Thye wanted to know Gods Name and He told them Exodus 3;13-15 saying His name is Jehovah forever and when Jesus has cleaned out satan Gen 3;15 he will submit to Jehovah who then becomes all things to everyone 1st Cor 15;28

No.  Abraham's God is Jesus Christ.  See Genesis 15:6 and John 8:58.  Islam rejects the truths that the Lord Jesus Christ is God, so islam leads to hell.  Here is what is true:  Death leads to immediate heaven or hell, and it is too late to be saved, after death.  To be in heaven and not hell, believe in the Lord Jesus Christ, who is God and who died on the cross and shed His blood to pay for all of our sins in full, and who was buried, and who resurrected from the dead.  The only way to avoid hell is by believing in the Lord Jesus Christ, without adding any of your own works.  See Romans 4:5, 1 Corinthians 15:3-4, and John 3:16.

Jews, Christians and Muslims all worship the God of Abraham, and have the Adam and Eve, Noah's Ark and Moses myths.

They claim they do. Christians and Jews disagree.