[exim] Exim4 smarthost configuration help (debian)

Hi all.

First of all, let me start saying that I'm a total nb as far as mail server
administration is concerned (it's not my primary job).

I have a linux machine (pallino.cace.local) on the internal network, behind
a NAT.

I want to configure exim4
- not to manage any local mailbox for the users on pallino.cace.local
- to forward all the messages directed to the local users to an external
SMTP server (mail.cacetech.com) external to the network
- to rewrite the local recipients and local sender with the addresses in
/etc/email-addresses (e.g. root: gianluca.varenni@???)

I configured exim4 as smarthost, forwarding the emails to mail.cacetech.com.
That works perfectly, including TLS authentication, i.e. if I run "echo foo
| mail -s test foo@???" the mail gets sent correctly.

The problem. The sender address gets rewritten properly (root -->
gianluca.varenni@???), the local recipient don't get rewritten
properly.

So if I run "echo foo | mail -s test gianlucav" the mail gets sent to
gianlucav@??? (instead of gianluca.varenni@???)

The update-exim4.conf.conf file is the following one

# /etc/exim4/update-exim4.conf.conf
#
# This is a Debian specific file

dc_eximconfig_configtype='satellite'
dc_other_hostnames='cace.local'
dc_local_interfaces='127.0.0.1'
dc_readhost='cacetech.com'
dc_relay_domains=''
dc_minimaldns='false'
dc_relay_nets=''
dc_smarthost='mail.cacetech.com'
CFILEMODE='644'
dc_use_split_config='false'
dc_hide_mailname='true'
dc_mailname_in_oh='true'
dc_localdelivery='mail_spool'

email-addresses is the following one

# This is /etc/email-addresses. It is part of the exim package
#
root: gianluca.varenni@???
gianlucav: gianluca.varenni@???

Can you point me in the right direction? I looked around for some easy guide
on it, but I couldn't find anything useful (maybe I'm just blind)?

Thanks in advance
GV