Integrated polarization converters (PCs) with high (>99%) conversion efficiency open up many new possibilities in an InP-based photonic integrated circuit. In this paper, we describe how such a PC can be added to a circuit containing semiconductor optical amplifiers (SOAs), in order to obtain polarization independent amplification. Polarization independence is obtained by placing the PC halfway between two identical SOA sections. This approach has the advantage that no compromises in design and fabrication are needed. The polarization conversion is found to be very high, above 99.5%, when using a tolerant two-section PC. The extra insertion loss due to the converter is below 0.5 dB. The polarization-dependent gain (PDG) of the SOA reduces from 17 dB to only 0.3 dB by the inclusion of the PC. This is comparable to the best PDG values found in the literature with other techniques. The reduction is achieved over the whole C-band and for varying pump currents.