What ever you do 'GUEST,Frustrated with BT customer service' don't, and I mean DON'T involve BT.
This is an internal extension (and therefore your equipment) so if you have BT come to fix your problem they will charge an 'arm and leg' and all the bits in between just to come and knock on your door. They then charge for their time, and parts. The ******** tried to charge us £200+ for 10 minutes work repairing their own equipment. It took 9 months of fighting and being shoved around 'Customer Services' (BT = Bullshit 'n' Transfer) before getting the charge dropped.
Assuming the old cable is in good condition crimping a new plug onto it is fine, other wise buy and feed in a new cable.