Office 365 Group External Email (Hybrid)

JamesH50 Yes we did get this resolved, but we did not do it ourselves as we had to use a vendor. I will reach out to them for a detailed explanation, but here is the idea of what they did:

They used a write-back feature in Azure to recreate the Office 365 groups created on the web in our on-site Active Directory. 

This made it so that when an external email went through our Exchange Server which serves as a relay, the email address existed and allowed it to then go to Office 365 where the actual group existed and distributed the email.

The reason I am not entirely sure how it works is because in AD the groups are called something like: Name: Group_70b9cd7-6f22-... Type: Distribution Group - Universal Description: {Group Name} Email Address: {Email Address}. There is an attribute labeled: msExchRequireAuthToSendTo that needed to be set to FALSE for some of the groups that still had problems. The groups are also placed in an Admin OU since they wont be used for anything except for a relay.

If you use some sort of support, maybe this will help then understand what needs to be done. If I can get a better explanation from someone who knows more than me, I will update here!