You wouldn't be able to actually do the registration from another site. You'd need to redirect the user's to a page on your site and, from there, the user could click Facebook login button. Facebook has restrictions on where their authentication popup can be called from and it *has* to be from your site.
With that said, in the new v5.2.1 or v5.2.2 release (I can't remember which), we did implement an option for server side (redirection) authentication. That doesn't use the popup and, possibly, could be used for what you're looking for since you could link to the registration flow URL and that would redirect the user to Facebook to authenticate. You can test that setting with the option in the Configuration -> Facebook area of JFBConnect.. it's called "Show 'Login Credentials' in popup". Feel free to test how authentication works on your site with that setting disabled and then see if that's how you'd want to redirect a user from another site to your page.
I'd probably recommend using a real landing page on your site instead though so that you can give the user more information about registering. If you just link to a registration page from a different URL, it may be confusing (or look like a phishing attempt) to the user.
I hope that helps explain,
Alex
Link to Facebook registration?
