Perhaps someone can explain me here a better way but the only way I found to to this now is as follows. Suppose we have two submodules with bases A and B of M defined by M.submodule(). Suppose moreover B is a submodule of A and both are of finite rank. Then we have to lift the basis of B as per (in this case A and B are the same)
sage: A.quotient_module([A.retract(b.lift()) for b in B.basis()])