When configuring an Exchange 2010 hybrid environment a Receive Connector is created on the Exchange 2010 server. This Receive Connector is configured with the FQDN entered in the Hybrid Configuration Wizard (see previous blog post on Exchange 2010 Hybrid) and the source IP addresses of the Microsoft Exchange Online servers. If one of these servers access the Exchange 2010 environment, they end up on the Office 365 Receive Connector (based on the IP address) and the correct SSL certificate is returned. This way mutual TLS is established between Exchange 2010 on-premises and Exchange Online.
It sometimes happens that the wrong certificate is used for SMTP communication between Exchange on-premises and Exchange Online, thus resulting in SMTP mail flow failure between the two.
You can check this in the Exchange Admin Center (EAC) in Exchange Online. Logon to the EAC in Exchange Online, select Mail Flow and click the Connectors tab. You’ll see two connectors. One connector for mail from Exchange 2010 to Exchange Online, and one connector for mail from Exchange Online to Exchange 2010.