Internal and external address problem

[Rose]

Running Exchange 2000 on a server for domain users.
Unreachale from outside.
Domain is DomainA.

Users have 2 addresses :
To...@DomainA.com for internal mail
To...@TheCompany.com for external mail

Ha...@DomainA.com for internal mail
Ha...@TheCompany.com for external mail
etc.

Using a POP downloader for incoming mail from outside.
And using an SMTP relay to our ISP for sending out any mail for which it
can't find an address internally.

Now, we have come across a problem that must be well known by seasoned
Exchnage users :
Three users: Tony and Harry are local and Mary is outside.

Tony sends a message to Ma...@OutsideComapany.com and puts Harry on CC so he
can have a copy.
To do this, Tony opens his Global address book and clicks Harry in as CC.

Mary in the Outside company receives the message. Fine. No problem.
Then she sees that a copy was sent to Harry and she wants to contact Harry.
The name in CC is just "Harry " not Ha...@TheCompany.com nor
Ha...@DomainA.com

Mary sends her message to Harry and gets an Undelivered message saying that
the address Ha...@DomainA.com is invalid.

What's the solution ??

Thanks in advance.
Postings only please.

Seamus