This paper introduces an innovative guidance and control method for simultaneously capturing and stabilizing a fast-spinning target satellite, such as a spin-stabilized satellite, using a spinning-base servicing satellite equipped with a robotic manipulator, joint locks, and reaction wheels (RWs). The method involves controlling the RWs of the servicing satellite to replicate the spinning motion of the target satellite, while locking the manipulator's joints to achieve spin-matching. This maneuver makes the target stationary with respect to the rotating frame of the servicing satellite located at its center-of-mass (CoM), simplifying the robot capture trajectory planning and eliminating post-capture trajectory planning entirely. In the next phase, the joints are unlocked, and a coordination controller drives the robotic manipulator to capture the target satellite while maintaining zero relative rotation between the servicing and target satellites. The spin stabilization phase begins after completing the capture phase, where the joints are locked to form a single tumbling rigid body consisting of the rigidly connected servicing and target satellites. An optimal controller applies negative control torques to the RWs to dampen out the tumbling motion of the interconnected satellites as quickly as possible, subject to the actuation torque limit of the RWs and the maximum torque exerted by the manipulator's end-effector.