You have which new socket, the sensor end or the vehicle end?

If it is just a case of joining the two separate wires I would think that two splices with crimp and solder connections would work fine, then wrap it to protect it. It is just a continuity loop.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue