cable too short to reattach into a sturmey archer 3 speed shifter I've just been given a Rayleigh Chiltern. The only problem is, the cable has unattached from the gear shifter. I Googled how to re thread, but the cable isn't long enough at the top end to slide right into the length of the shifter - it barely fits inside the shifter at all. 

Can I use the excess cable at the hub end (if so how?) or am I just doing something wrong? Never done this before, so any advice would be massively welcome.
Cables have special ends on the brake lever / shifter lever side which you need in order to hook the cable into the lever. A brake cable end for mountain bikes looks like:



You can't add these ends to an existing cable. If the cable is broken near the lever, then almost surely the part of the cable with the end is not going to be long enough. Thus, if you don't have a cable end, buy a new cable.

It's quite dangerous to have a broken brake cable, so you should get that fixed asap. 

If you do have the appropriate cable with end, you just need to remove the cable tension (disconnect it), and then thread it through the part of the lever which can grab the cable as shown here.