Hi Pastor,
Based on your description, I understand you can't receive the emails sent by the external users.
To troubleshoot the issue, please use a hotmail mailbox to send a test email to check whether this issue persists.
If yes, please send the detailed non-delivery report (NDR) to me. I have sent a private message with a subject of < Website not showing up after migration to Office 365 ) > to you.
To access the private message:
-Go to your details section on the right side of the community site.
-Click Private messages.
-Click the subject title of the response to read the message
Best regards,
Jerry Cen