They can start by getting Google and other major app stores to pull the app for copyright / trademark infringement on the term "iMessage", then they can sue the developer for the same (he's public with his identity).

Beyond that all they need to do is include some form of digital signing in the login process which he can't duplicate and jobs a good un.

Alternatively they may say that they don't care and leave it alone as it strengthens iMessage as a platform.

But my guess is that this won't end well. Isn't it trademarks that you have to defend or you lose them? If that's the case then Apple at the very least need to have him change the name and so on.