When the Send As permission exists, the Send on Behalf permission will not work, so you just need to add the send as permission.
About send as permission, you need to add from both Exchange online and Exchange on-premises:
Run the following command in the Exchange Management Shell on your on-premises Exchange server:
Add-ADPermission -Identity EXO1 -User ONPREM1 -AccessRights ExtendedRight -ExtendedRights "Send As"
Then run the corresponding command in Exchange Online PowerShell:
Add-RecipientPermission -Identity EXO1 -Trustee ONPREM1 -AccessRights SendAs
For more detailed information, you could have a look about this article: Mailbox permissions and capabilities NOT supported in hybrid environments
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