You’d need to go into the database and find all of the custom fields and change the post id they are associated with. Not really an easy task. There isn’t any way to do this automatically.
Even more of a reason to use an options page, then where ever they want them to show you just need to move a little code without changing anything.
The client wanting to move these things around, to be honest, leads me to think that a custom post type for FAQ’s might even be a better choice.
