Thanks a lot for your reply, Tim.
1) Create the file with the applet the user has loaded inside its Moodle course. Save this file locally, in the user's computer (for that, the applet must be signed, of course).
3) Use a Java code from the applet to run a php code in the server computer. This php code could then take the previous file, stored in the predefined folder, and (linking with the Moodle 2.0 file picker) upload it to the user's private file repository.
Still, I would have liked to do it without the need of a ftp server running on the Moodle computer but that does not seem possible at the moment. Anyway, I still have to figure out how can I put step 3 into practice.
I'll post any advance I make related to this topic.