The steps work for Outlook 2013 and 2016. Illustrations are from Outlook 2013.
In Outlook choose the File tab > Info > Add Account
In the E-mail Address field enter the address of the account you want to proxy into
- When prompted do not just fill in your password. Select Use another account and enter your NetID and Password
(Optional) Uncheck Use Cached Exchange Mode
Sent/Deleted items are placed in the proxied mailbox's folders.
New emails created while in the proxied mailbox are addressed from the proxied mailbox.
From field may be changed to the shared mailbox.
Replies from the proxied mailbox are addressed as if sent by the shared account automatically.