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Are you getting any outside email? Did you add all the DNS records to your pubic DNS server?
Office 365 BLOG
Before moving on, can you please help me to clarify the issue with some questions?
- What domain are you currently using, your own domain or onmicrosoft.com?
- If you are using your own domain, have you properly add all DNS record?
- Does this happen to the emails from all outside domain or a specific domain?
- Did the sender receive any NDR?