JFB + new website adress

Florian,
Yes, you should just be able to update the Facebook Application's website and domain URL's to be the new URL. Once set (it may take up to an hour or so to take effect), when user's click the Login w/ FB button on the new site, it will be just like the old one. No new approvals or anything. The old site will no longer work with logins though, so I wouldn't recommend keeping that up.

One thing to note though, if you're using Like buttons, Comments, etc. Those will not transition to the new site. Each of those is 'connected' to a specific URL, including the domain, so those will be lost. Additionally, you should make sure if you're using any of the modules or {JFBCLike} type tags, you should update the URL's in those to use the new domain.

Hope that helps prepare you, and good luck with the new site!
Alex

Yep, definitely agree with the tests. Something you can try, actually, pre-move is to create a new Facebook Application, set it up to all the new site's information, and simply use that for testing. JFBConnect doesn't care about the app your using, just as long as Facebook says the user properly authenticated it. So, during testing, the user would need to authenticate, but then should be logged into their existing/current Joomla account from the old site.

Hope that makes sense.. and allows you to do some better testing without switching Facebook App settings, and temporarily breaking your current site to do so.

Good luck,
Alex