Lift the module out of the headphone cup, leaving all wires attached.

Clip the two wires circled in orange.

Now that the speaker is free set it aside.

Clip the two wires circled in yellow.

Replace speaker module and solder it to the two wires circled in orange.

Now solder the speaker wires (circled in yellow) back to the module.

For soldering see the ifixit soldering guide: How To Solder and Desolder Connections