====== Exchange 2016: client does not have permission to send as this sender ... ======
The message does not appear completely but seems to be **"550 5.7.1 Client does not have permissions to send as this sender"**. Obviously the user does have the permissions (the user was the owner of the mailbox itself).

Run AdsiEdit and select the following path:
  * Configuration – Services – Microsoft Exchange – <MY_ORG_NAME> – Administrative Groups – Exchange Administrative Group – Servers – <MY_SERVER_NAME> – Protocols – SMTP Receive Connectors:
  * Properties of the “Client Proxy <MY_SERVER_NAME>” receive connector, “Security” tab and grant the “Accept Authoritative Domain Sender”  allow permission for the “Authenticated users”.

Restart server