I just had a quick look to see if there is a simple file copy command - there isn't.
You would need to open the file and read it in chunks that would fit into arduinos memory and write them to the destination - this would be a fairly simple loop once you have got all the other bits sorted.
They do have a product VF2F as a proof of concept that copies all the jpegs off one memory device into a unique folder on a usb memory stick in the other socket.
If you email them they might let you see the code (couldn't see a download in readable form on the site).