I've often heard this claim been said by many people, not as a criticism of Islam, but merely as a theory for the origins of some of the religion's teachings. To a lesser extent, people also say it about Judaism and Christianity. Some of the supposed similarities are dualism, the theme of good and evil, the existence of God and the devil, heaven and hell, a final war between good and evil, which seem to be generic from me and don't prove that Zoroastrianism had any influence on the Quran. When Muslim armies invaded Persia, there's no historical documentation they were interesting in studying or borrowing any of their beliefs. Are there any teachings and stories that you believe were possibly borrowed from Zoraster? I think it's an interesting claim, but I can't find any proof either way.
Muhammed was orphaned very young and then traveled all over the Levant and Mesopotamia... I would assume he was an observant young guy and probably thought about all the stories he heard on his travels.
A lesser extent? I don't think that it is in coincidence that most Jewish scriptures are dated to around the time that Cyrus of Persia feed the Israelite people. Hell, the Bible even calls Cyrus a Messiah. I think those things are only "generic" today because of the the huge influence Zoroastrianism has had on the modern world, through Judaism and Christianity. But yes, I think Zoroastrianism has had as much influence on Islam as it has on every other Abrahamic religion.
