This paper presents fully kinetic particle simulations of plasma charging at lunar craters with the presence of lunar lander modules using the recently developed Parallel Immersed-Finite-Element Particle-in-Cell (PIFE-PIC) code. The computation model explicitly includes the lunar regolith layer on top of the lunar bedrock, taking into account the regolith layer thickness and permittivity as well as the lunar lander module in the simulation domain, resolving a nontrivial surface terrain or lunar lander configuration. Simulations were carried out to study the lunar surface and lunar lander module charging near craters at the lunar terminator region under mean and severe plasma environments. The lunar module's position is also investigated to see its effect on the plasma charging relative to the craters. Differential surface charging was clearly resolved by the simulations. For the charging of a lunar lander module made of conducting materials, the results show a near-uniform potential close to that of its surrounding environment and moderate levels of local electric fields. Additionally, the risks associated with charging and discharging increase significantly under a more severe plasma charging environment as shown in the severe plasma environment cases.