Hi @Mountain Pond ,
Based on your description, I want to confirm if you want your mail routing flow in below scenario: Internet mails - Barracuda -O365 -On-prem? Please correct me if I misunderstand your issue.
As far as I know, if you want to internet mails flow to O365 first, you should disable centralized mail transport. Detailed information on routing incoming Internet messages through the Exchange Online organization for your reference.
In addition, please refer to a blog on How to Configure Microsoft 365 for Inbound and Outbound Mail, and it indicates that you only need create one send connector to configure outbound mails. In the blog, it also mentions that each of your domains from which you want to be able to send email must be added to the Barracuda Email Security Gateway. Be sure to add all of your accepted Microsoft 365 domains to the Barracuda Email Security Gateway before configuring outgoing email in this section.
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