Hi,@Carlos Amaral
Thanks for posting your question in the Microsoft Q&A forum.
Based on your description, you have a hybrid environment where users are synced to Azure, the member in Azure can send on behalf, the user locally cannot, and both members have rights to send on behalf.
Referring to the official Microsoft documentation,some changes are needed on your Microsoft Entra Connect server for Send on Behalf permissions to sync between your on-premises Exchange servers and Exchange Online.
You can refer to this URL for details: Permissions in Exchange hybrid deployments | Microsoft Learn
If my answer is helpful to you, please mark it as the answer so that other users can refer to it. Thank you for your support and understanding.