There's no way to elevate an already running process, so you have to encapsulate that in a separate EXE and run that with elevated permissions.
This could be as simple as creating a batch file and in there use the 'runas' command.
runas /noprofile /user:mymachine\administrator myexe.exe
Then run the batch file from your main VFP executable.
The problem with this is that it's inelegant and prone to prompting for credentials.
You could try doing it in VFP code using the Windows API:
Download the Win32API project from https://github.com/VFPX/Win32API
Extract somewhere and run apiviewer.exe
Search for 'how to start a process as another user'
That should display a VFP program illustrating how to leverage the Windows API to do it. And you're in a world where you now have to worry about the password being stored in plaintext in your program :)