Put some soldering tin on the endings of the deinsulated cables

unsold the original cable from the earphones

As you can see the right connection has a red dot. This is where you have to sold the cable that carries the signal(In the first picture the insulated one)

Arrange the cables before soldering like in the second picture. This formation seems like the best to fix the cable best

Sold them and put everything together again. Try this http://www.youtube.com/watch?v=e8ODm-F9-... to find out where to clip them into the rack again :)