I think you need to do a lot more than that. You won't have all the synchronized recipients in the other company's AD (Exchange) so it won't know how to route the mail to the corresponding mailboxes in Exchange Online. If you just create a
send connector that routes your domain to your Exchange server, and they don't define your domain in their Exchange organization as "Authoritative", then everything should work as it's configured. The MX routes mail to their Exchange server,
which routes it to your Exchange Server, which routes it to Exchange Online.
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