Corollary 1

Let M be an isotypical A-module of type S. For every A-submodule N of M, identify Hom$_A(S,N)$ with the linear subspace of Hom$_A(S,M)$ consisting of the mappings with image contained in N.

a) The mapping $N\mapsto$ Hom$_A(S,N)$ is an isomorphism of ordered sets from $\mathscr{D}_A(M)$ to $\mathscr{D}_D$(Hom$_A(S,M)$).

b) The inverse bijection sends a linear subspace W of Hom$_A(S,M)$ to the submodule $\sum_{h\in W}h(S)$ of M.

This is a reformulation of Theorem 2 when we take $(V, \alpha )$ to be the canonical description of M.