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The influence of the stimulated Raman scattering in the four-wave mixing process in high birefringent fibers is theoretically analyzed. We consider the dual pump configuration in both co-polarized and orthogonal polarization schemes and treat simultaneously the stimulated Raman scattering and the four-wave mixing processes. The obtained results are valid even when the shift between the pumps and signal lies inside the Raman band. Results show that when the phase-matching condition is achieved the generation of the idler wave is mostly dependent on the real part of the fiber nonlinear response function, whereas the amplification of the signal wave is mostly dependent on the imaginary part. Results also show that when the phase-matching condition is satisfied the optical power evolution of the signal and idler waves for small frequency detunings are mostly described by the anisotropic Raman response of the fiber, whereas for high frequency detunings the isotropic response dominates. Our analysis also shows that the stimulated Raman scattering can increase the efficiency of the four-wave mixing process, for certain frequency detunings.