First off, i feel sorry for A for needing the gratification of having the fish as 'his' rather than 'ours'. similarly, i think B is just being a tool for claiming a capture that was largely the result of A's hard work.
anywho, thats largely irrelevant. i guess if you want a concrete verdict the best place to look is the IGFA
most certified world records are the accomplishment of a team: the skipper, deckie and angler.
although the angler gets all the credit, the other member of the team are integral components in the successful capture and as such are equally responsible for the record. despite this, the angler is largely the only one recognised as being associated with the caputre.
i don't know why this is so, and even though its pretty sucky, its the rules
so i guess technically it's B's
nonetheless, any fisho with a shred of integrity will acknowledge other people's captures (however undeserving) and get over it
aero has a good point too btw