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Sophos Central Email and Exchange Hybrid Configuration

Hello Everyone:

We just completed deploying Exchange Hybrid between our On-Premise Exchange 2016 U17 and Exchange Online. And migrated one mailbox to Exchange Online. All seems to work, until we noticed that there are some emails between the Exchange Online user to On-Premise users that are not being delivered. On-Premise to Exchange Online seem not affected. Incoming and outgoing emails from/to Exchange Online to/from external recipients are working. Same is true with On-Premise Exchange users. It’s just between On-Premise and Exchange Online users.

Our previous setup was: Exchange 2016 and ALL incoming and outgoing emails goes through the Sophos Central Email Gateway. We only have one Exchange 2016 server.

On another note, which option is the easiest to configure in Hybrid setting?  And if these are even possible?

First Option: Route everything to Sophos Central Email Gateway then Exchange Online > On-Premise Exchange and vice-versa.

Second Option: Route everything to Sophos Central Email Gateway then On-Premise Exchange > Exchange Online and vice-versa.

We are leaning towards the first option. But either options, we are curious how emails route between users of Exchange Online and On-Premise? Any send/receive connectors between these two systems we need configure or create?

Thank you all for any assistance and insights.