Show sent emails in inbox outlook

Outlook 2016:

Policy Path: User Configuration/Administrative Templates/Microsoft Outlook 2016/Outlook Options/Preferences/E-mail Options

In the dialog box for the policy setting, select Enabled to enable the policy and select the Save copies of messages in Save Items folder option.

The Registry keys associated with the Save copies of messages in Sent Items folder option are as follows:

Where <x.0> is your version of Outlook:

Outlook 2016, Outlook for Microsoft 365 and Outlook 2019 = 16.0
Outlook 2013 = 15.0
Outlook 2010 = 14.0
Outlook 2007 = 12.0

DWORD Value Name: SaveSent
Value Data:

0 = Disabled; Sent emails aren't saved in the Sent Items folder.
1 = Enabled; Sent emails are saved in the Sent Items folder.