Hi Jason,
Since you can relay emails to internal uses in your domain, you should have completed the configuration of IIS for the relay with Office 365. And I’d like to collect some more information for further investigation:
1.Could you let us know which Office 365 account you are using for the relay?
2.Can you send emails to Gmail or Yahoo directly from the Office 365 account in Outlook Web App? If not, please provide the entire NDR message.
3.After we completed the IIS configuration, we can perform a test to see if the relay services works fine referring to the “How do you know this worked?” at the bottom of the following article: https://technet.microsoft.com/en-us/library/dn592151(v=exchg.150).aspx . So could you run a further test for both an internal email and an external email at your convenience? If the SMTP server can’t deliver the messages, non-delivery reports (NDRs) will be created in the C:\InetPub\MailRoot\BadMail folder.
Please let us know the results together with the NDR messages as well.
4. Moreover, as an Office 365 global admin we can trace the mail flow using Massage Trace in Exchange admin center. Please make sure your admin role has got Organization Management, Compliance Management, and Help Desk permissions in Exchange admin center-> permissions-> admin roles.
Before running the trace, please try to resend emails to an internal and external user from the account and then filtered by the email account. You can view the detailed status of the email deliveries by double-clicking the entries.
Please also provide the screenshots of the detailed trace results as shown below after trying those steps.
Consider the requested information may contain your privacy, I have sent you a private message. You can provide the information by replying to it. To access the private message, please:
1. Go to the Your details section on the right side of the community site.
2. Click Private Messages.
3. Click the subject title of the response to read the message.
To upload the screenshots, you can click Use rich formatting when replying and then click the Insert image button.
Best Regards,
Alex