Adapting two-way radio tactical throat mic (laryngophone) to cell phone or laptop
Let's get a couple of things together here.

First, a diagram of how to connect the Kenwood connector:



That image came from here.

Second is how to connect to an Android phone:



Your throat microphone is most likely a two terminal electret microphone, so Note 2 from the Kenwood diagram should apply and there will not be a 10uF capacitor in the microphone line.

All you should need to do is to connect the microphone line from the headseat to the Android microphone line.  Then the microphone ground to the Android ground.  The microphone ground is the ground connection on the smaller (2.5mm) plug.

The Android diagram shows where to connect the microphone wires. 

Once the microphone is connected and plugged in to your phone, the phone should recognize the headset and switch to headset mode.

That should do it.   

Connect the earphone to left or right and ground if you need the earphone.



If you've never used a throat mic before, then you should be ready for a surprise.

Throat mics don't sound like regular microphones.  Throat mics pickup pretty much just the vibration from your larynx.  All the aspirant sounds ("S" and "Sh" sounds and the like) will be very weak or not present at all.  People may have a hard time understanding you.