A colleague of mine put together a nice summary of how cloning and sharing works across workspaces, which I thought might be a useful guide to share.
How Do I Clone Assets Across Workspaces?
For assets that aren't templates, its best to clone them as local assets inside of a program. With the proper access level, you can drag and drop these assets into another workspace:
To move assets to a new workspace, put them into a folder and drag the folder over to the other workspace.