Let M be any preradical for ] and N any module in ]. A
module N is called M-lifting if for every submodule K of N, there is
a decomposition K = A  B, such that A is a direct summand of N
and B  M(N). We call N is (strongly) FI-M-lifting if for every fully
invariant submodule K of N, there is a decomposition K = AB, such
that A is a (fully invariant) direct summand of N and B  M(N). The
class of FI-M-lifting modules properly contains the class of M-lifting
modules and the class of strongly FI-M-lifting modules. In this paper
we investigate whether the class of (strongly) FI-M-lifting modules are
closed under particular class of submodules, direct summands and direct
sums.