if member A sends and instant message to member B and member B does not acknowledge it (whether thay are talking to someone else or they just signed off), the IM should convert to an email in member B's mailbox so that they can view and answer it at a later time.

But if a member A sends IM to a member B and member B doesn't reply, then member B will see a yellow box on the sidebar informing him about the IM message from the member A. This works like that in the current version. Please, check the demo.