The Horyu-VI nano-satellite is an international lunar mission with the purpose of studying the lunar horizon glow (LHG)—a still unclear phenomenon caused by electrostatically charged lunar dust particles. This study analyzes the mission trajectory with the hypothesis that it is launched as a secondary payload of the NASA ARTEMIS-II mission. In particular, the effect of the solar gravity gradient is studied; in fact, depending on the starting relative position of the Moon, the Earth, and the Sun, the solar gradient acts differently on the trajectory—changing it significantly. Therefore, the transfer and lunar capture problem is solved in several cases with the initial Sun-Earth-Moon angle as the key parameter. Furthermore, the inclination with respect to the Moon at capture is constrained to be equatorial. Finally, the problem of stabilization and circularization of the lunar orbit is addressed in a specific case, providing an estimate of the total propellant cost to reach the final orbit around the Moon.