Smoked L322 3rd brake light on a l320

[Bmbar]

Hi guys I’m struggling to find a smoked 3rd brake light for my 2007 l320. There are loads of light’s available for the l322 and I believe they are identical in shape and size and they only differ with the connection. My question is is it possible to use the connection off the original light and stick it on the l322 light.
Cheers
Barry