Detected but doesn't work? Does it work without the extension?
Is your extension two cables or one? Is your headset two cables or one?
I'm guessing your headset only has one cable for both the mic and headset. This is called a 4 pole 3.5mm.
4 pole is what allows it to carry left, right, mic, and ground at the same time. If you look closely you can see that it has an extra band on the plug than a standard headphone does.
All you should need is a 4 pole extension.
https://www.amazon.com/StarTech-com-3-5mm-Position-Headset-Extension/dp/B008DWGLLO
Keep in mind that your computer probably doesn't have 4 pole connectors on every slot. Usually green = audio, pink = mic, and black = 4 pole (both).
You may need a 4 pole splitter if your PC doesn't have a 4 pole connector.
http://thumbs1.ebaystatic.com/d/l225/m/mjTnny4O2FmsvLhuNNj3iyA.jpg
This splits your 4 pole connection into two 3 poles.