The Schr?der-Bernstein Theorem for sets is well-known. A dual of
the Schr?der-Bernstein Theorem is that two sets with surjection maps onto each
other are isomorphic. there is a question that when Schroder-Bernstien property holds for modules. In this thesis, we investigate the dual of the schroder-Bernstien Theorem in the category of modules.