Unfortunately I did not take any pictures of the headset before I cracked it open and dug out the guts. It was just snapped together, though, and I was easily able to open it by twisting gently with the blade of a knife stuffed into one of the side joins. What I wanted was the main board, so I could get access to the bits I wanted to extend:
the single button
the charging jack
In the photo, the button is on the other side of the board so it is not visible.