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Huh, interesting! It's a 3-pole to 4-pole 3.5mm patch cable. No telling how it's actually wired, but you could try using a normal 4-pole 3.5mm audio cable (with three rings, four sections on the plugs). If that doesn't work, you can try bridging two sections of one of the plugs with a little bit of aluminum tape.
Note that this isn't super likely to work, unless it's just Jakks Pacific's goofy way of making you buy a special cable. If the wiring's ordered differently between the two plugs, you might have to get brave and start cutting and twisting.
