You're likely looking for a replacement Xbox 3.5mm Headset Adapter, not a communication cable. This small adapter connects a standard 3.5mm headset (like the Tritton AX 720) to the Xbox controller.
Unfortunately, the original Xbox 360 Headset Adapter is discontinued and replaced by the Xbox Stereo Headset Adapter (USB) for newer consoles.
If using a newer Xbox (Series X|S), you'll need the Xbox Stereo Headset Adapter instead.