In previous versions of Exchange, our preferred way to have users share a resource (or shared) mailbox is to grant Full Access, and Send As permission to that mailbox from the Exchange Management Console.
If that exists in 2016, I can’t find it. But powershell can help.
To grant those same permissions in 2016, using a powershell session connected to the Exchange 2016 server, type
Add-MailboxPermission -identity "firstname.lastname@example.org" -user "email@example.com" -AccessRights FullAccess -InheritanceType all Add-AdPermission -identity "Mailbox, Shared" -user ralph.hogaboom -extendedRights "Send As"
Of course, you’ll have to have added the Open These Additional Mailboxes in Outlook first. Then restart Outlook and you should be set.