Hi Brett,
The forwarding rules and settings cannot be migrated from on-premises to Office 365. Given this situation, please set up a forwarding email address by using Powershell or Exchange Admin Center (aftering add the external email address as a mail contact).
You can get more detailed information about "configure mail forwarding for a mailbox" from this link: http://technet.microsoft.com/en-US/library/dd351134%28v=exchg.150%29.aspx
Thanks,
Edward Qu