Islam is only 1700 years old, King Solomon lived 2800 years ago. Kind of hard to be a member of the foremost religion of hate and murder when it wont exist for another 1000 years! Such is the stupid revisionist history of the religion of peace i.e. hate!
I agree with you. Muslims don't.
From their POV all the prophets of the Old Testament as well as Jesus were good Muslims. (Not sure what they believe about Paul and the other apostles.)
Islam did not, from this perspective, come into existence with the teachings of Mohammed. It was the faith of all believers in God prior to him also. Mo merely purified and finalized the faith.
From this perspective, Judaism and Christianity are deviations from and heresies of Islam, the primitive pure religion. This is somewhat similar to the way many Protestants view Catholicism as a corruption of the original Christian faith, and their own sects as a return to that original doctrine. Or what Mormons believe about all other Christian groups.
Now this isn't something I agree with, but since Muslims believe it, it is not at all illogical for them to claim Adam, Moses, Noah, Solomon and Jesus as good Muslim prophets.
I believe it's untrue, but it's not illogical.