During maneuvers of a space manipulator system (SMS), thruster fuel in its spacecraft (S/C) results in sloshing effects which impact its dynamics and performance. In this work, sloshing effects are modeled by a 3D mass-spring-damper. A novel system identification scheme is developed, which identifies all parameters required for the reconstruction of system dynamics despite the unmeasurable sloshing states. This is achieved by two identification experiments. In Exp. 1, the SMS translates with locked joints allowing for the elimination of the unmeasurable sloshing states. As a result, all sloshing model parameters and the mass of the SMS base are identified. In Exp. 2, the SMS operates in free-floating mode, with the reaction wheels (RWs) and the manipulator(s) active. Based on kinematics and conservation of momentum, a method is developed which eliminates the unmeasurable sloshing states and identifies all the required SMS inertial parameters. The estimated parameters render the system dynamics fully identified and available to advanced model-based control algorithms. The effect of sloshing parameter errors is also discussed. The developed scheme is validated by simulation and experiments.