Frequently Asked Question

By default, items deleted from a shared mailbox in Outlook go into the Delegate's own Deleted Items.

1. This behaviour can be changed on a per-user basis only, based on that user's registry setting. 
2. Run the following PowerShell commands as the user:

New-Item -Path "HKCU:\Software\Microsoft\Office\16.0\Outlook\Options" -Name "General" -Force

Set-ItemProperty -Path "HKCU:\Software\Microsoft\Office\16.0\Outlook\Options\General" -Name "DelegateWastebasketStyle" -Type DWord -Value 4 -Force

3. Close and re-open Outlook.

The "-Value" parameter can be:
4 - put in the Shared Mailbox Deleted Items
8 - put in the Delegates own Deleted Items.