is it possible that works?
phbb2 to coppermine and then coppermine to mambo.
coppermine can either autenticate users against/with mambo or phpbb, not both of them. You will either have to modify mambo to authenticate against phpbb or vice versa. Can't tell you how to accomplish this, as I'm not familar with those apps. I suggest you ask this on the mambo support boards (make sure to search first, may have been asked already).
Joachim