  It has been shown that singlet Cooper pairs can be converted into triplet
ones and diffuse into a ferromagnet over a long distance in a phenomenon known
as the long-range proximity effect (LRPE). This happens in materials with
inhomogeneous magnetism or spin-orbit coupling (SOC). Most of the previous
studies focus on the cases with small SOC and exchange field. However, the
physics was not clear when SOC and exchange field strength are both much
greater than the disorder strength. In this work, we consider a two dimensional
system with a large Rashba-type SOC and exchange field in the case where only
one band is partially occupied. We develop a generalized quasiclassical theory
by projecting the Green function onto the partially occupied band (POB). We
find that when the SOC energy scale is comparable with the exchange field,
there is no LRPE. The reason is that the nonmagnetic impurities together with
the large SOC and exchange field can effectively generate spin-flip scattering,
which suppresses the proximity effect. We also show that when increasing either
SOC or exchange field, the decay length of superconducting correlations can be
significantly increased due to an approximately restored time reversal symmetry
or spin rotation symmetry around the $z$ (out-of-plane) axis.
