This study investigates optically injected semiconductor lasers at period-one dynamics for conversion from non-orthogonal to orthogonal optical single-sideband modulation signals possessing high optical modulation depth and broad microwave frequency tunability. The highest microwave frequency demonstrated up to 40 GHz is mainly restricted by the electronic bandwidth, not by the proposed conversion scheme. A higher microwave frequency, such as 100 GHz or more, is feasible. Only a typical semiconductor laser is required as the conversion unit. After conversion, the microwave phase quality, including the linewidth and the phase noise, is mostly preserved. In addition, simultaneous microwave amplification of more than 10 dB is possible, which results from the considerable enhancement of the optical modulation depth.