The invention provides an end part (1) for connecting a control cable (2) of a transmission of a motor vehicle to a connector ball joint (3) that is part of a shifting lever or part of the transmission (3). The end part (1) comprises a recess for receiving a connector part (7) which is used for covering and connecting the ball joint (3). When an axial force is exerted on the cable (2), the connector part (7) received in the recess can abut against an elastomer damping damper (11) inserted between the connector part (7) and the inner wall of the recess. According to the invention, the end part(1) comprises a rigid stop means arranged to limit the movement of the connector part (7) and the elastic deformation of the damping damper (11).