The invention relates to the mechanical adapter assembly of the transmission line for a motor vehicle. The mechanical adapter includes shafts rotatably guided by different bearings and couplings for driving said different shafts. The mechanical adapter also includes a differential carrier, which is used in the form of a crankcase containing the oil for lubricating the different bearings and couplings and provided with a front aperture. A front plate integrates a pump and makes it possible to close said front aperture of the differential support. Additionally, an attached pipe section supplies the oil from said front plate to the differential support and interacts with additional fixtures to the front plate and the differential carrier.