View the original community article here
Last tested: Dec 14, 2020
An embed user cannot "move" or "copy" a dashboard into another space/folder, since those functions are only available on the folder page in the UI and are not available in the "four squares" embed folder dropdown menu.
Therefore, the Manage Access / Edit permission on a folder will give embed users the ability to *save* content to their folders (i.e. from a query created on the explore page), but not to move/copy.