Isomorphisms between injective modules

Suppose that (F,M) is an injective structure of R-Mod such that the class F is closed for direct limits, then two modules in M are isomorphic if there are maps in F from each one of the modules into the other. Examples of module classes in such injective structures include (pure, coneat, and RD-) injective modules, as well as τ-injective modules for a hereditary torsion theory τ. Thus providing a generalization of a classical result of Bumby's and two recent ones by Mac\'{i}as-D\'{i}az.