Use a soldering iron to solder the edges of your new cable wires.

Plug your new cable into a compatible device and check the wires are working by ensuring voltage using a multimeter.

Desolder the old wire from the speaker and solder the new wire to the speaker with the same color until the old cable connection wires are completely removed and the new cable connection wires are soldered to the speaker.

For more information on soldering, visit this guide.