  Recently, some fast radio bursts (FRBs) have been reported to exhibit complex
and diverse variations in Faraday rotation measurements (RM) and polarization,
suggesting that dynamically evolving magnetization environments may surround
them. In this paper, we investigate the Faraday conversion (FC) effect in a
binary system involving an FRB source and analyze the polarization evolution of
FRBs. For an strongly magnetized high-mass companion binary (HMCB), when an FRB
with $\sim100\%$ linear polarization passes through the radial magnetic field
of the companion star, the circular polarization (CP) component will be induced
and oscillate symmetrically around the point with the CP degree equal to zero,
the rate and amplitude of the oscillation decrease as the frequency increases.
The very strong plasma column density in the HMCBs can cause CP to oscillate
with frequency at a very drastic rate, which may lead to depolarization. Near
the superior conjunction of the binary orbit, the DM varies significantly due
to the dense plasma near the companion, and the significant FC also occurs in
this region. As the pulsar moves away from the superior conjunction, the CP
gradually tends towards zero and then returns to its value before incidence. We
also investigate the effect of the rotation of the companion star. We find that
a sufficiently significant RM reversal can be produced at large magnetic
inclinations and the RM variation is very diverse. Finally, we apply this model
to explain some polarization observations of PSR B1744-24A and FRB 20201124A.
