The goal of this work is to develop a functorial transfer of properties between a module \(A\) and the category \({\mathcal M}_{E}\) of right modules over its endomorphism ring, \(E\), that is more sensitive than the traditional starting point, \(\mathrm{Hom}(A, \cdot )\). The main result is a factorization \(\mathrm{q}_{A}\mathrm{t}_{A}\) of the left adjoint \(\mathrm{T}_{A}\) of \(\mathrm{Hom}(A, \cdot )\), where \(\mathrm{t}_{A}\) is a category equivalence and \(\mathrm{ q}_{A}\) is a forgetful functor. Applications include a characterization of the finitely generated submodules of the right \(E\)-modules \(\mathrm{Hom}(A,G)\), a connection between quasi-projective modules and flat modules, an extension of some recent work on endomorphism rings of \(\Sigma\)-quasi-projective modules, an extension of Fuller's Theorem, characterizations of several self-generating properties and injective properties, and a connection between \(\Sigma\)-self-generators and quasi-projective modules.