Point MX record to Exchange online or Exchange on-premises are all ok, for more detailed information about it, you could have a look about this article.
About adding a new domain in hybrid, you could follow these steps below:
- Add this domain name to Exchange on-premises admin center as an accepted domain.
- Then use an Email address policy to apply it on mailboxes. You can also add new email address to those mailboxes manually.
- Add this new domain name as alterative UPN suffixes from Active Directory Domain and Trusts. Then you will could change UPN for those old mailboxes.
- Migrate those mailboxes from Exchange on-premises to Exchange online.
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