Hey, we are trying to set up our Exchange server, and everything is fine for our licensed users. But we also have other emails for special tasks like invoicing, maybe we gave away some emails to friends and family. And when we set up our Exchange server, all those emails stopped receiving. Is there a way to only touch the licensed users, and let the unlicensed users go to our previous mail host, like a fallback?
Mailbox owners need licences, period. (Shared mailboxes don't, but won't be much good without interactive users to read them.) If your extra addresses use different domains then simply drop those domains from your accepted domain list and move the MX records back to your old host. However, if as I expect your extra addresses use domains you do want to transfer to Exchange Online, then what you are asking for is something called a split namespace. It's a complete can of worms; horribly insecure and hard work to maintain - don't go there.