61 13... Circular connector, 20-pin, system D2.5
WARNING: This page is about a different car, the 2011 BMW 750xi, 2011 BMW 750Lxi, 2010 BMW 750xi, and 2010 BMW 750Lxi. However, it is still accessible from the selected car via links, so may be relevant.
Carefully press back retaining tabs (1) of internal connector (2).
Turn internal connector (2) until retaining lugs (1) snap into release groove (3).
With special tool 61 0 303 press down retaining hook (4) of corresponding contact and pull out cable.