Lifting modules as a main concept in module theory have been studied and investigated extensively in recent decades. The first author in [1] tried to consider and investigate this concept with a homological approach. Let R be a ring and M be a right R-module. Then M is called I-lifting if image of every endomorphism of M lies above a direct summand of M. In this paper, we are interested in studying modules M with the property that ϕ (F)/D≪ M/D for every endomorphism ϕ of M and for some direct summands D of M, where F is a fixed fully invariant submodule of M. We call such modules IF-lifting. We provide some examples of IF-lifting modules as a proper generalization of lifting modules. Some characterizations of IF-lifting modules are given. We also define relative IF-lifting modules to study direct summands and finite direct sums of IF-lifting modules.