Let D be a principal ideal domain (PID) and M be a module over D.We prove the following two dual results:(i) If M is finitely generated and x,y are two elements in M such that M/Dx≌ M/Dy,then there exists an automorphism α of M such that α(x) =y.(ii) If M satisfies the minimal condition on submodules and X,Y are two locally cyclic submodules of M such that M/X ≌ M/Y and X ≌ Y,then there exists an automorphism α of M such that α(X) =Y.