[exim] Different addresses for local and outgoing mail

I've a mail address for outgoing mail with a national provider (@tele2.it)
and a second mail address for my local mail (@debian). Using Mutt, it's
possible to set two different sender name, so that, when I
send an external mail, in the header of message is it possible
to read my external address, while when I send a local mail,
it results my local address. In .muttrc I use the following hook:
send-hook .* 'my_hdr From: Mauro Sacchetto <mauro.sacchetto@???>
send-hook '~t @debian$' 'my_hdr From: samiel <samiel@debian>
However, it doesn't work, for even local mails have, in the headers,
the external address as sender. So I suspect that exim4 rewrites
Mutt indications, using the address written in /etc/email-addresses.
Is it possible to set two different account in exim to obtain
the result I'd like?

Thanx
MS

-- 
Prof. Mauro Sacchetto
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e-mail: mauro.sacchetto@???
        mauro.sacchetto@???
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