grey wire broken at batterie connector

Repairing my MacBookPro (end of 2006) a light grey wire broke, which is soldered to the connector for the batterie.

Guess the soldering on that white connector is so fine, that I can not fix this with a "normal manual" soldering job.

The machine works fine.

What purpose has this light grey wire?

What hardware function do I loose?

What can go wrong with my MacBookPro?

Can the entire connector with the wires be replaced?

(Would like to attach a picture, guess this is not possible)

Thanks for the help to everybody.

The case can be closed.

As the Mac works with this wire broken/disconnected....

....so I do not know what hardware function do I really loose.