As ResidentLurker said, simply moves the saves via a flash drive. However, saves have their own folder in C:\Users\<User>\AppData\Roaming\RenPy\Harem Hotel, not the launcher folder. It's why they're completely safe when updating; by being separate from the game files, so you can delete them without worry. Only on android do you need to move the saves when updating.
There does exist a code to max characters' stories, but 1) it's Patron-exclusive, and 2) comes with a bunch of issues, which it warns you about in advance.
I must have installed mine differently than most people, as my saves folder is located inside my game folder. This is the path to my saves folder <C:\Users\Pzycho\Desktop\Nightmare Fuel\Harem_Hotel-v0.13.2-pc\game\saves>.
It seems my computer is using a different structure than most people, I don't even have an AppData folder in my Users folder, lol.
That's odd, I went and double checked my user folder to see if I had enabled show hidden for it before, and had to enable it. I could have sworn I set my entire computer to show all hidden files previously, but for some reason it didn't seem to land there properly. Now I wonder what other files it didn't affect...