Recuva as a 'slave' drive

I use the term 'slave' drive as a general term. I suppose as a SATA Drive it is an additional drive, and not a 'slave' drive.

I removed the SATA Drive from my HP all in one desktop and put it in a desktop at work. When I run the recuva through its paces, it tells me that a whole bunch of files are unrecoverable because the name or path has changed, as the drive is now an "F" Drive instead of a "C" drive. I would like to recover the files before I put it back in my old computer and redo the whole computer.