But if you have made two distinct modules perhaps you have some reason to get them separated. If so it looks strange that you have a call inside moduleB that referes to something in moduleA.

Is My::Module::Another somehow a particular logic subset of My::Module ?

Anyway when you import subs from a module is no longer needed to call them specifying the full package: asub1 must suffice(instead of a fully qualified My::Module::asub1 )

I'm not the best advicer on modules design here around but perhaps you can get deeper in your description and in what these modules really represent.

PS take a look to Proper way to create packages and re-usable code? where some Anonymous like you give some good suggestion about design of modules and separation/aggregation of concerns.

L*