Make Postfix modify sender address?

Hello!

My setup is basically like this:

Client -> Relay1 -> Relay2 -> Relay3 -> Destination

On the "Client" system and on the "Relay1" system, I've got
postfix installed; Client: 2.2.5 @ HP-UX 11.11, Relay1: 2.3.2 @ Linux.
On "Client", I've setup a cron job for root and in /etc/mail/aliases, I've got:

root: alexander@skwar.name

So, mails to root@client will be redirected to alexander@skwar.name.
When the cron job now produces some output, a mail is generated and
sent to my adress (alexander@skwar.name). Everything just as expected.

My problem is, that the mails don't arrive at the "Destination"
system, because the "Relay3" system doesn't relay those mails. It
rejects with: "sender domain must exist". Yes, that's true - sender
domain doesn't exist in the Internet, it only exists in the "LAN".
Systems up to "Relay2" are in the LAN, "Relay3" and "Destination"
are in the Internet.

Can I somehow configure the "Relay1" system so, that it modifies the
From: adress if it matches certain criteria (like, it matches a given
adress)?

I CANNOT change the setup so, that "Relay1" or even "Client" directly
send to "Destination". It has to go over "Relay2". I've got no control
at all over "Relay2" or "Relay3".

Thanks a lot,

Alexander Skwar
--
The old complaint that mass culture is designed for eleven-year-olds
is of course a shameful canard. The key age has traditionally been
more like fourteen.
-- Robert Christgau, "Esquire"