I tip my mage's hat to Arkane Studios for placing Prey's save files in the Saved Games user folder. Virtually no other developers do this, preferring instead to litter the Documents folder or stash them somewhere under the hidden AppData folder.

Unfortunately, the GOG version of Mooncrash doesn't do the same. Web searches turned up nothing: everyone pointed out the aforementioned folder. Since I had to resort to sifting through Process Monitor's log, I thought I'd share:
<parent installation folder>\Prey\Whiplash\USER\SaveGames
I intend to back up the parent folder, which includes a Profiles folder and a game.cfg file.

If you installed the game under the Program Files folder, then it wouldn't have write permission to its installation folder unless you run it in administrator mode. In this case, you should find the files under %LocalAppData%\VirtualStore\ instead.

Dude, you should know that your post helped me even after 2 years.

I spend my previous evening trying to find my save files to no avail as they weren't in either folders.

What I managed to do is deactivate the cloud sync which makes them appear under the following path :

C:\Users\<My Username>\Saved Games\Arkane Studios\Prey\SaveGames\Campaign<number>