The German transmission manufacturer later acquired by Magna that supplied manual and dual-clutch gearboxes to BMW and Ford was Getrag.
Founded in 1935, Getrag became one of Europe’s major transmission specialists. Its products included conventional manual gearboxes, automated manuals, and dual-clutch transmissions for passenger cars and performance models. The company’s broad catalog covered both longitudinal and transverse layouts, allowing it to work with different engine and drivetrain configurations.
Getrag supplied BMW applications including manual gearboxes and the 7DCI600 dual-clutch transmission used in several BMW M models. It also produced transmissions for Ford, including the MT82 manual gearbox and the 6DCT450 dual-clutch unit marketed in Ford applications as PowerShift. These examples explain why both manual and dual-clutch technology appear in the question.
Magna International completed its acquisition of Getrag in 2016, after announcing the deal in 2015. A common mix-up is ZF Friedrichshafen, another major German transmission maker with extensive BMW connections. Aisin and Eaton are also important suppliers, but Getrag is the manufacturer matching all of the clues.