Replacing a broken 3.5mm audio jack with a different one, why does each cable have different amount of wires?
Either purchase a bare 3.5mm Tip Ring Sleeve plug or salvage the plug from a stereo cable.  The green plug that you show in your picture looks to be for a microphone intended to be plugged into an old Sound Blaster audio card or old-style PC.

You might be able to salvage the TRS plug from the green connector by cutting all of the plastic away from the plug itself.  There is a good possibility that all three contacts are available once all of the plastic is cut away.  Use heat-shrink tubing to cover the connections.

Although there is not a standard for wire colors, most often the white wire is connected to the Tip and the red wire connected to the Ring.  Shield goes to sleeve.  You can confirm which wire is connected to the Ring on the broken plug by using an Ohmmeter.