A module for a system for driving and synchronizing a countershaft of a transmission gearbox. The module includes a coupling device having an input element intended to be rotationally coupled to a reversible electric machine and an output element intended to be rotationally coupled to the countershaft. The coupling device has a coupled state in which the clutch device is able to transmit torque between the input element and the output element and an uncoupled state in which the input element and the output element are uncoupled. Also included is a lock-up device which has a lock-up state in which said lock-up device blocks the rotation of the input element of the clutch device, and a released state in which said lock-up device allows the input element to rotate.