If you move a Dropbox file on another device like your smartphone or in the browser while having it opened in an application on your computer is a bad idea.
The computer cannot track this movement because the Dropbox client on your computer deletes the old file and recreates it in another place. For your computer it’s a different file altogether.
Consecutive saves of your opened file would either fail and you’ll be puzzled why, or you implicitly save to the old location and end up having two versions of the same file in your Dropbox without knowing it.
Having two different version of the same file in different locations is a call for trouble. Better close the file on your computer before moving it to another place.