How to do an in ear headset driver transplant?

I was wondering how to do the soldering, since the wire from the headset i already own is one long copper wire with a spiraling black stripe seemingly painted on, with a thread in the core of the wire. Would i just lay the two wires next to eachother and solder between them?

If you remove the external insulating sheath you'll find the wires inside consist of many very fine strands of 2 different colours - or 3 between the stereo plug and the Y-junction. Each strand is insulated with a layer of coloured enamel which should melt in the molten solder, though it takes patience. Very gently scraping the end of a bundle of strands with a knife before soldering can help, though it's extremely easy then to break some of the strands. (A few doesn't matter.) Some people suggest passing the end of the bundle through a flame to burn off the enamel.

You also need to arrange some kind of strain relief to prevent strain on the solder joints if the wires are pulled, such as an extra piece of wire bundled with the join, and the whole join can be covered with PVC tape, or much better, mouldable glue such as Sugru (sugru.com).