All links should consist of the full URL because:
a) It's related to security;
b) there is basically no easy way to recognize relative links correctly;
c) it's better for search engines to provide full links.
If you move forums to another domain, you just need to replace all older domain links in posts by the simple SQL command like this:
update minibbtable_posts set post_text=REPLACE(post_text,'http://www.olddomain.com','http://www.newdomain.com') where POSITION('http://www.olddomain.com' IN post_text)>0;
That way we have also replaced all internal links on our own forums when we have moved miniBB project from minibb.net to minibb.com.