Jesus was a Jew, so He could bring Judaism to perfection. Mohammed was a pagan - neither Christian nor Jew - so there's no continuity there.
In other words, Mohammed and Islam are simply wrong.
Which is why, if he were here today, he would probably "freak out" if you were to share with him your definition of "perfected" Judaism.
And Jews think Christians are simply wrong. Doesn't mean we can't like each other and work together on matters of mutual interest.