In order to efficiently perform particle simulations in systems with widely varying magnetization, we developed a drift-Lorentz mover, which interpolates between full particle dynamics and drift kinetics in such a way as to preserve a physically correct gyroradius and particle drifts for both large and small ratios of the timestep to the cyclotron period. In order to extend applicability of the mover to systems with plasma frequency exceeding the cyclotron frequency such as one may have with fully neutralized drift compression of a heavy-ion beam we have developed an implicit version of the mover. A first step in this direction, in which the polarization charge was added to the field solver, was described previously. Here we describe a fully implicit algorithm (which is analogous to the direct-implicit method for conventional particle-in-cell simulation), summarize a stability analysis of it, and describe several tests of the resultant code.