In case you trying to sent e-mails outside your company using anonymous authentication, you have to run the below commands from Exchange Management Shell.
- Find your receive connector you want to use (ex. Default Frontend EXCHANGESERVER) and execute below commands:
Set-ReceiveConnector "EXCHANGESERVER\Default Frontend EXCHANGESERVER" -PermissionGroups AnonymousUsers
Get-ReceiveConnector "EXCHANGESERVER\Default Frontend EXCHANGESERVER" | Add-ADPermission -User 'NT AUTHORITY\Anonymous Logon' -ExtendedRights MS-Exch-SMTP-Accept-Any-Recipient
Done!