This chapter focuses on the study of the influence of solar radiation pressure on the dynamics around the dynamical substitutes of the \(L_1\) and \(L_2\) points in the Earth-Moon Quasi-Bicircular Problem. This dynamical model is a periodic perturbation of the Restricted Three Body Problem that incorporates both the gravitational effect of the Sun and the solar radiation pressure acceleration on the sail. Beginning with the simplest invariant objects in the Quasi-Bicircular Problem, namely, the dynamical substitutes of the two equilibrium points and extending to the low-order Sun-resonant periodic orbits with the synodic period of the Sun, we explore the evolution of families of resonant periodic orbits as two sail parameters, defining orientation and efficiency, are varied. The study reveals a complex network of connections between these families. In the analysis, we include their characteristic curves, the maximal Floquet exponent, and the linear normal behavior of the periodic orbits. An interesting observation is that, for certain parameter values, periodic orbits exist that become stable under the influence of solar radiation pressure acceleration.