I could not see staff in your screen shot , open the small lock by authenticating admin password , you have deleted staff ( selected and clicked over minus sign ) , again click on plus sign a pop up window appears in users and groups if you see staff semi greyed , click over it to highlight and click on select , in my screen shot staff is not visible as I do not deleted ( in users and groups section ) in the last click on apple for enclosed items .
The permissions should be exactly the same in screen shot , when your Mac and other devices like iPhone / iPad and another Mac are signed in with same Apple ID and password , exactly on your network documents and file sharing will automatically start syncing .
However if you plan to send document with mail , right click over the document in finder > share the mail application opens fill up " To " and other credentials( drag and document from finder to desktop again drag and drop to mail app window and send mail Send an email in Mail on Mac - Apple Support . may be the other devices are not necessarily synced , their mail address can be example 1 @gmail.com

