The gain-transparent stimulated Brillouin scattering (SBS) process has been successfully applied to dual-orthogonal-pump four-wave mixing (FWM) to enhance the performance of polarization-insensitive wavelength conversion. The Brillouin pump and Stokes waves control the optical phase of one of the FWM pumps to achieve phase matching to extend the wavelength conversion range. The experimental data show that the polarization-insensitive property is well preserved under gain-transparent SBS processing, and only 0.5dB output power variation is observed in the converted idler. A 5.1dB enhancement of the conversion efficiency is obtained through the phase control at large signal-pump spectral spacing. By applying this scheme for exclusive phase control, simultaneous polarization-insensitive and wideband wavelength conversion can be potentially realized in other configurations using two copolarized pumps or a polarization diversity loop.