Position a wire to the corresponding connection point on the jack.

Carefully apply a small amount of solder to hold the wire in place.

Repeat this for each wire.

Make sure to reference the mapping of wires to connection points that you created in Step 4.

When soldering the wires, be patient and meticulous about getting the right position to make a good connection.

If the internal wires do not have their own insulation, use a small bit of shrink tubing on each wire. This will prevent them from shorting across another wire.