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Hi Erick - thank you again for the reply.
I think I have managed to find the solution though.
Through much trial and error it seems, as most things are, it is permissions related.
The ability to create Remote Mailboxes via the Exchange EAC in a hybrid exchange environment is to make sure the user trying to make the change has at least Exchange Organization Management membership on the on-premise environment.
The O365 online role based permissions for the same user does not seem to make much difference in this scenario at all. I tried with Global Admin and with basic User role and as long as they are member of the Organization Management on-premise group they can both create remote mailboxes as well access the Exchange EAC via "Enterprise" and "Office 365" tabs in the EAC
I also think the user needs to be a member of the Recipient Management group but I haven't done enough testing to confirm nor deny this guess.
I must say that this is somewhat disappointing as I would like to give some junior members of my IT team permissions to create these remote mailboxes but now I have to basically give them the key to the castle as with Organization Management they get full access to break/change/modify almost anything. Not ideal...
I'm surprised there isn't better granular permissions in this regard and equally surprised there is so little information on the net regarding how and what is needed to do something so "every day" as create a user and mailbox in an exchange hybrid environment.
*scratches head*...