Earlier quoted context omitted.
Islam is generally considered an Abrahamic religion. There is a lot of continuity; the (very very) short version of the Islam perspective is "Abraham explained God's will to us, then Jesus was sent by God to explain God's will better, and then finally God sent Mohammed and he communicated God's will perfectly". Three time's the charm I guess? Many of the figures you know from the Bible make their appearance in the Qu…
Yep, I know that, but it doesn’t offer anything else than a claim to authenticity, by posing as a continuation, while the previous revelations are then discarded. The mentions of Biblical persons and events, as I hinted in the previous comment, are cultural rather than theological, and can’t be used to establish theological continuity, no matter how hard the Ismaelite genealogy is pressed.
Can't the same argument be raise for Christianity? I'm sure at the time of Jesus he saw himself as rectifying Jewish practice (and of course there are the passages where he says that the old laws are still in force), but pretty quickly Christianity was modified and sold to gentiles (thanks to Paul, who never met Jesus and wrote 13* of the 27 books of the New Testament) and the Mosaic laws were mostly set aside.
The whole idea of "fulfillment theology" is that Jesus fulfilled the old covenant and established a new law. That is why Christians eat pork and so on.
* everyone agrees that three of those 13 weren't actually written by Paul, and three more are in various degrees of doubt