Adrian, you'll need to download the s1fwx tool from the tools section of this site. Here's a link to it:
http://mympxplayer.com/dload.php?action=file&file_id=15
Click on download button near the bottom of the page.
Connect your friend's player to the usb port. Then open the s1fwx folder and click on extract.bat. The tool will detect and display the driver letter. Select that driver and the tool will extract the full firmware as a dump.bin file.
Then connect your player and upgrade with that dump.bin
***By the way, do make sure that your friend has the firmware that's similar to the original firmware you had on your player or else you might end up killing your player and you'll have to open it up to short circuit.
You said you have a backup firmware: How did you backup your firmware? Any reason in particular why it doesn't work when you try to recover your player? What's the message that the upgrade tool gives when you try to recover with the backup?