Let M be a finitely-generated module over a Noetherian ring R. Suppose 𝔞 is an ideal of R and let N=𝔞M and 𝔟=Ann(M/N). If 𝔟⫅J(R), M is complete with respect to the 𝔟-adic topology, {Pi}i≥1 is a countable family of prime submodules of M, and x∈M, then x+N⫅∪i≥1Pi implies that x+N⫅Pj for some i≥1. This extends a theorem of Sharp and Vámos concerning prime ideals to prime
submodules.