Set up Auto BCC in Outlook 2016

You can do effectively the same thing as auto-BCC with a new rule.  This one works for me:

1. Go to the "home" tab of the ribbon/toolbar
2. Click the "rules" dropdown and select "Manage Rules & Alerts"
3. From the "Rules and Alerts" dialog box, select "New Rule"
4. This pops up a "Rules Wizard" with a number of templates in it.  Pick "Apply rule on messages I send", and hit "Next".
5. The next dialog shows conditions, leave all unchecked and hit "Next".  You'll get the warning "This rule will be applied to every message you send", hit "Yes".
6. The next dialog lets you select what to do with the message - check next to "move a copy to the specified folder".  At the window in the bottom of this dialog you'll see the line "move a copy to the specified folder" appear, click the underlined word "specified", from the resulting dialog pick your Inbox and hit "OK".
7. The next dialog lets you pick exceptions, click "Next" again.
8. The final dialog lets you name the rule, make sure "Turn on this rule" is selected.  The rule showing in the bottom window should read
   1. "Apply this rule after I send the message"
   2. "move a copy to the Inbox folder"
9. Click "Finish" and the new rule will be created.
10. Hit "OK" one more time to leave the "Rules and Alerts" dialog.

Best of luck...