Hi Brett,
Thanks for your updates.
If you want the messages to be copied to the user's mailbox, you can set it by using PowerShell command and EAC. Please use one of the following ways:
1. Run "Set-Mailbox -Identity "user" -ForwardingAddress "external mailbox" -DeliverToMailboxAndForward $true".
2. In EAC, please tick the "Deliver messages to both forwarding address and mailbox" check box.
Best Regards,
Edward Qu