This work proposes a novel dual-stage control strategy for a Flying Capacitor converter. During transients, the proposed control scheme applies Finite-Control-Set Model Predictive Control (FCS-MPC) to drive the system close to the desired reference, including all the known non-linearities of the system in the converter model. When the converter state is in a neighborhood of the reference, the dual-stage controller switches to a PWM-based linear controller with an integral action. In this case, the linear controller is reformulated in its feedback form. Thus, the internal linear controller states can be updated based on the actual input applied by the predictive controller. This allows the dual-stage controller to achieve a smooth transition when commuting between controllers and a zero steady-state error even when load parameter errors are present. Experimental results are provided to verify the effectiveness of the proposed dual-stage controller.