How to move a file from within the app to another folder?
Drag protocol can be a bit confusing, however, it does follow a recognisable pattern…

To the same volume  


Drag will move - unless the file is in a protected location [root level of the volume, or in a protected System folder], in which case it will copy  
 Opt ⌥  drag will copy  
 Cmd ⌘  drag will override the simple drag behaviour for protected files &amp; move instead [but will need Admin authentication].


To a different volume  


Drag will copy  
 Opt ⌥  drag will copy  
 Cmd ⌘  drag will move [ie, copy, then delete the original.]


So,  Opt ⌥  always copies, but  Cmd ⌘  reverses the default behaviour of just dragging.

Worst case scenario - you can change your modifier key &amp; check the added icon on the file you're dragging to see your end result, right up until you let go of the mouse button.

Just to complete the set -  Cmd ⌘   Opt ⌥  dragging will make an Alias at the destination.

edit …&amp; after all that I realise that Preview will not adhere to that behaviour… Move appears to not be an option at all.
Best guess is that you cannot move an open document &amp; even hope that an app could keep track of where it went.
The Finder can. You can move the file in the Finder whilst open in Preview, but then Preview will tell you you are working on a copy &amp; you need to save a fresh version.
Pretty safe &amp; sensible behaviour, really.