Decompositions of homomorphisms of abelian p-groups with p²-bounded target

Let p be a prime. We classify homomorphisms H:V₁→ V₂ between abelian p-groups that are direct sums of cyclic groups, under the assumption p²V₂=0. We prove that every such homomorphism is isomorphic to a direct sum of finite indecomposable representations and that this decomposition is unique up to isomorphism and reordering of the summands.