Yes, though you must have more than one client in your account and you can move complete folders not individual files.
In order to move a folder go to Content->Media Library, and open your main folder until you see the desired folder. Right-click on that folder to get to the secondary menu and select Copy to Client.
Select to which client you will be copying the folder to and click the Copy button to confirm.
* The images used in this guide are for illustrative purposes only and designed to be a representation and/or general orientation of the required steps and/ or existing system and are not in any way designed to represent or guarantee aspects of the project, software and or information from any particular unit or location.