Unfortunately, in your scenario, the SharePoint Designer can't help!
To be able to copy document to another document using SharePoint designer, you should have a workflow on the source document library to can (
Copy item + Then delete) to the destination document library as shown below:
Note you can use
Call HTTP Web Service action to copy a document to another document library Using REST, but unfortunately, this action is not available in SharePoint Workflow 2010.
For more details check unable to copy all documents from one library to another
So in your case, the available workaround is using
Event Reciever to can easily control the moving process based on the document URL.
For more details check Programmatically Copy and Move documents in Sharepoint 2010