perldoc -f do, perldoc -f require, perldoc -f use. If you ask me, you are better off making B.pl a real module, but then if it's really called like that, then don't call it B.pm, since the latter already exists and is in core.

All in all it's hard to suggest you a good strategy without knowing what A.pl and B.pl really do. For sure what you're asking is awkward, as such, and most people will smell a XY Problem here.