Start by wedging the phone plug in a contraption like the PanaVise^® shown here.

Melt a small pool of solder on the shield contact as shown.  Tilt the contact down so solder runs away from the tip.

Here's a top view of the solder pool.

Next, prepare the end of the cord:

1. Remove about 5/8" (16mm) of the cord's outer jacket
   
   
2. Unbraid the cord's shield to expose the center wire.
   
   
3. Strip about 3/16" (5mm) of insulation from the center wire.
   
   
4. Twist together the strands of the shield.  Cut them so they reach only to the end of the center wire's insulation.
   
   
5. Pre-tin the conductors
   
   
6. Hook the center wire through the plug's tip contact as shown on the right.
   
   

DON'T FORGET TO SLIDE THE PLUG'S HANDLE ONTO THE CORD BEFORE SOLDERING!

Solder the center wire first.  The shield has more wiggle room and you can solder it down where it relieves strain on the center wire.

To attach the shield, first  bring the pre-installed pool of solder to the melting point with your iron.  Then set the pre-tinned shield into the melted pool of solder.

Use your other hand to hold the cord still until the solder cools.

Don't take too long with this step.  The shield can get hot enough to melt the center wire's insulation, causing a short.

After the metal is cool to the touch, bend the strain relief tabs over the sustain pedal cord's outer jacket as shown here.

Screw on the handle and you're done.