associated sequence is a short exact sequence iff the original sequence is a split short exact sequence.

Question

Let $0 \to L \to M \to N \to 0$ be a sequence of $R$-modules. Then to prove that the associated sequence $$0 \to Hom_R(D, L) \to Hom_R(D, M) \to Hom_R(D, N) \to 0$$ is a short exact sequence of abelian groups for all $R$-modules $D$ if and only if the original sequence is a split short exact sequence.