We used modulating retro-reflector (MRR), hybrid frequency-phase-keying (FPK) modulation, and Reed-Solomon (RS) code technology to improve the performance of the terrestrial-satellite laser communication link. A system using FPK modulation and RS codes based on the Fisher-Snedecor (F) distribution atmospheric turbulence model is proposed for the MRR-assisted terrestrial-high-altitude-platform (HAP)-satellite laser communication, in which MRR is installed on the HAP. The laser beam without signal is transmitted to HAP through the forward path. The MRR loads the optical signal from the terrestrial-HAP link onto the optical carrier, which is then reflected back to the satellite terminal along the backward path. The combined effects of light intensity scintillation of atmospheric turbulence, beam wander of uplink, atmospheric attenuation, pointing error, and HAP random jitter on the terrestrial-HAP (equipped with MRR)-satellite (T-HMRR-S) laser communication link are considered. The expression of the BER of RS codes and FPK modulation (RS-FPK) system under weak atmospheric turbulence is derived and compared with terrestrial-HAP-satellite (T-H-S) system with different modulation and without MRR. At the same time, the effects of modulation coding parameters, zenith angle, the field-of-view angle, and the coverage area of the MRR on the performance of the T-HMRR-S system are simulated and analyzed. The simulation results show that the T-HMRR-S system using RS-FPK technology has better performance. These works provide a theoretical basis for the research of modulation coding technology of T-HMRR-S link systems.