Address Rewrite does not work in scenario Exchange 2003.
It works in the following scenario:

After the edge subscription and synchronization,
Enable-TransportAgent -Identity "Address Rewriting Inbound agent"
Enable-TransportAgent -Identity "Address Rewriting Outbound agent"
Restart-Service MSExchangeTransport
New-AddressRewriteEntry -Name Good.will -InternalAddress good.will@work.com -ExternalAddress good@vanarts.com
https://test1.work.com/owa and login as good.will@work.com.
Send e-mail to Kaiming.Liao@gmail.com
The message shows the sender of good@vanarts.com. But e-mail to Kaiming@vanarts.com will be disappeared. I think it is filtered.