That is a power button for your PC. It looks like you need to hook up the rear port for the plug. That plug in your pic does not go directly in your mobo but in the back panel of your PC.
https://www.amazon.com/JM-202-Power-Button-Switch-Module/dp/B00MQIBWF6
I have a feeling that you are going to have a hard time finding an extender for that just because it carries USB and on/off connections to the mobo all in one. You would have to reach out to the OEM of that device to see if they make an extender.