well, in general, you should have right, left, and mic, with a ground for each on the iphone end, and all 3 will have a common ground. for the headphones, right and left, with a ground for each, and ground is shared.
you will want to remove the protective coating with a microtorch or other heat source, solder and heatshrink, as opposed to twist together. You will also want to look up the pinout for the iphone side of it, and use a continuity tester to identify what each cable usually is.
red is USUALLY right, blue or green is is usually left - the white on the sennheiser is unusual (i double check this either by following the cable to the end, or using a temporary connection with crocodile clips between a prepared, tinned end of the headphone cable and jack).
Red to red, white to green, and 'copper' to 'copper' should do the trick. all 3 have the pesky coating, so you'll need to remove it.
this is the exact process/tools that have worked for me in the past - but instead of the jack, tin both ends, press to check, then solder.
Are you going to have the AC jack (power entry module) on your new back plate? If so, what kind of terminals does it have on the inner side? A photo or a pencil sketch of your new back plate could help us visualize the problem.
Without knowing anything else, I would recommend splicing the wires with a crimped butt terminal (like this one or this one). It's a thin-wall metal tube inside of an insulating plastic tube. Each end of the tube can be crimped onto a wire. Here in the US, you can get them in any hardware store. Crimped connections are less brittle, compared to soldering.
Splicing plus soldering works too. Heat shrink is a more reliable insulation than tape.
Best Answer
They are just essentially string to help support the cable. You should be fine soldering the cable.
One thing to remember about the cables in headphones is that it is usually enamel coated copper wire. You usually need to heat it up to around 390*C to burn off the insulation before you can make a decent solder joint. The way I do this is to put a large blob of solder onto the end of a soldering iron, then push the end of the wire that needs to be tinned through the solder and pull it back out again. This usually neatly removes the enamel and tins the wire on all sides making soldering easy.
Bonus info, when more than one of the wires is broken midway along the cable, the easiest thing to do is the cut each of the wires at staggered locations so that when you solder them you don't need to worry about insulating one wire from another as the solder joints will be at different locations and the enamel on the other wires will be intact on the other wires. If you are soldering on a new plug though, you don't need to worry about that.