Searching USB cable with 4-pin connector
Forget all that. Just get a USB-A male to USB-A female extension. If you want it to be more permanent then put some heatshrink around where the two cables mate.

But if you really want to know, my bet would be one of JST's 2.0mm "Wire to Board Crimp Style Connectors. Possibly the PH (EDIT: actually now that I look at the other 2.0mm pitch connectors, it's definitely the PH).

http://www.jst-mfg.com/product/detail_e.php?series=199



I found this by going to JST's website and "Searching By Application or Series" and then choosing "Wire to Board Crimp Style Connectors" and then finding the part of the list where the 2.0mm pitch was located and looking at the images. Took about 5 minutes. Would take much longer for someone unfamiliar since their website sucks which seems to be par for the course for most connector manufacturers but JST is especially bad even by their standards.

To make use of this you would need to get a USB-A on one end and "bare wire" or "no connector" on the other end from Mouse or Digikey so you can crimp to it.