You're kind of stuffed on this one because of the over-molded strain relief. The white flexible material is probably used to keep the soldered wire ends and the wire itself all vibrating at the same level & frequency. Because of the vibration, that would ensure a longer life for the connection.
As Bob D. suggested, If you don't have the tools needed this repair will not be free.
![Smile [smile]](https://www.festoolownersgroup.com/Smileys/default/smile.gif)
You'll need a chisel point soldering iron in the 30-35 watt range.
Some rosin core solder, do
NOT us flux core solder!
While not absolutely necessary, a soldering iron stand is a welcome accessory. When hot, the iron will be in the 450º to 475º range. Because of the form and the stiff electrical cord, the irons have been known to roll around on the table and burn wood, plastic and anything else they come in contact with. They also sometimes roll off the table and land on your leg (that really hurts) or on the carpet/floor.
If you purchase good quality tools, Ungar or Weller, you're probably looking at a $50-$75 purchase price. Ungar & Weller are owned by the same company. I'm sure there are cheaper alternatives out there but I'm unaware of what they are.
I'm going to show in pictures what Jiggy said in words.
![Big Grin [big grin]](https://www.festoolownersgroup.com/Smileys/default/biggrin.gif)
Here's a photo of a 33 watt Ungar iron with a chisel point tip. This is what you'd use for your repair. The chisel point maximizes the amount of heat that goes into the solder connection.
Also shown is a 25 watt Weller with a needle point tip. It's used for LEDs.
A Weller soldering stand & a roll of resin core solder complete the photo. I think the solder alone was $20.
These hand irons are usually purchased in 3-pieces. The handle...the heating element...the solder tip. You choose each item.
The yellow sponge on the soldering stand is kept moist and is used to remove excess solder from the tip and to keep the tip clean for maximum heat generation.

Here's what Jiggy was talking about. Two small pieces of heat shrink, one for each solder connection and a single large piece to cover both solder connections. That produces a nice looking professional result.
The individual heat shrink pieces need to be some distance from each solder joint. The iron's putting out 450º but the heat shrink will start the shrinking process at 200º. Put just enough heat into the solder joint to get a good connection, then remove the iron and cool down the joint by blowing on it. Slide the heat shrink over the solder joint and shrink the tubing. Then move to the next solder joint and repeat. Finally, shrink the large heat shrink over both solder joints.

A couple of final notes. Make sure the joint is cool before you slide the heat shrink over the connection. At times I've rushed the process and when I started to slide the heat shrink over the joint, there was still so much heat in the joint that the heat shrink tubing shrunk before I could slide it fully over the joint.
![Crying [crying]](https://www.festoolownersgroup.com/Smileys/default/crying.gif)
I prefer to offset the solder joints by 3/4"-1". There will be a slight bulge when the joints are soldered and covered with heat shrink. So 2 bulging connections next to each other produce a larger bulge in the finished product. Offset them slightly and the cord will be straighter and look better.
Let us know what path you decide to take.
![Smile [smile]](https://www.festoolownersgroup.com/Smileys/default/smile.gif)