Hello everybody! I am having a super simple issue that I cannot seem to find a way to google the correct answer.

I had a 40mm fan with a 3 pin connector that I broke on my GeeeTech Prusa i3. Simple enough to replace I thought but a larger 3 pin connector fan came, apparently there are different types of 3 pin fans. Ok, no biggie... but how do I find a proper adapter/extender with one end at the right size? My gt2560 arudino/reprap hybrid board takes the tiny 3 pin connectors.

I got a good quality fan and am trying to find out how to search on amazon for the proper type of extender/adapter so I can connect it to my board. I need a couple feet long extender since it will be attached to my extruder as the cooling fan. Tried striping the plug off the adapter and pluggin the wire in, bad idea cause it still doesn't function. The voltages/amps were the same from the replacement fan and mine but the adapters are just too different i suppose.

It seems to be the size and shape of a typical computer motherboard 3 pin fan connector but obviously I need that smaller 3 pin connector which has a name that is alluding me! Please assist!