Don't know that you can. Is there any chance that you can borrow another computer for someone, install the demo, convert the file and then transfer the converted .fp7 file to your computer for conversion to .fmp12 format?
The code that turns off the demo FMP apps is very well hidden and I have never seen the location revealed.
Deleting the FMP demo and reinstalling will not change the expiration.
You could install the demo on another computer and convert.
You could boot into a VM copy of your OS to run it.
You could open the database in FMP 5 and export the data.
You could ask someone to do the conversion.