The FileManager is only applicable to files in local storage or iCloud Drive.
To work with files in Dropbox, you need to use a Dropbox object. This object has convenience methods for reading and writing files, but no simplified methods for moving files.
Anything that can be done with the Dropbox API can be done with the Dropbox object using the rpcRequest method, but it does require knowledge of the working of the Dropbox API…so it’s not a beginner scripting task, I’m afraid.
I do not have any good examples to share at the moment, but possibly some one else does.