*- Unless I've missed something obvious -*

There doesn't appear to be an option to add an attachment from your Briefcase.

I've searched all of Zimbra and can't find it mentioned, so must be missing.

When I go to add attachment, there is a tab "My Computer", seems logical that a Briefcase tab here would be the solution.

Seems a bit pointless to download a file from the Briefcase, to only upload it again.