Module classes and the lifting property

Let R be a ring. A collection of R-modules containing the zero module and closed under isomorphisms will be denoted by X. An R-module M is said to be X-lifting if for every X-submodule N of M there exists A leq N such that M=A oplus B and N cap B is small in B [11]. In the present paper, we consider the question: Can we characterize X-lifting modules via objects of the class X?