Should I be able to see outbound emails? Currently, I can only see inbound.
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If you use an internal mail server e.g. Exchange for sending e-mails -> you have to config the Sophos UTM internal IP as smarthost there and you have to allow host based relay on the Sophos UTM for your mail server / exchange host. Than you´ll see inbound and outbound mails using Sophos Mail Manager.
Maybe you should not turn of your onPrem Exchangeserver, see here:
Why you may not be able to decommission on-premises Exchange even with cloud solutions | Born's Tech and Windows World (borncity.com)
Also with O365, you can use your sophos smtp-proxy with hybrid configuration, and yes maybe an cloud smtp-proxy would be a good way, too!
We're currently using a Hybrid set-up and mail from 365 to On-Prem turns up in our Mail Manager but tenant to tenant does not which I find very strange. Is there a reason for this?....Sorry to jump in on this thread... :)
Yes, of course! It worked as designed, mails between tenants/ exchange online users will always routed directly between exchange online servers
Why? Its easy:
source and targed mailservers are the tenants exchange onlineserver, so why an extra step between it with onpremise? Its the wrong way, if a mail from exchange online server will go trough on premise and than again back to the targed exchange online server.
so, this mails go never trough on premise.
example: in hybrid envoirment, if 2 O365 mailboxuser of same tenant write each other, it will not go trough onpremise exchange.