I needed 
to let PHP send mails from my webserver 
to my web app users. So I installed qmail on my Debian server:
sudo apt-get install qmail
I also updated files in /etc/qmail specifing my domain name, and then I run sudo qmailctl reload and sudo qmailctl restart:
/etc/qmail/defaultdomain # Contains 'mydomain.com'
/etc/qmail/defaulthost   # Contains 'mydomain.com'
/etc/qmail/me            # Contains 'mail.mydomain.com'
/etc/qmail/rcpthosts     # Contains 'mydomain.com'
/etc/qmail/locals        # Contains 'mydomain.com'
Emails are sent without any problem from my PHP script 
to any email address, using the standard mail PHP library.
Now the problem is that if I send mail from my PHP using 
[email protected] as sender address, I want that customer can reply 
to that address! And possibly, I want all mails sent 
to this address should be forwarded 
to my personal Gmail address.
At the moment qmail seems 
to not accept any incoming mail because of "invalid mailbox name". Here is a complete SMTP session I established with my server:
me@MYPC:~$ nc mydomain.com 25
220 ip-XX-XX-XXX-XXX.xxx.xxx.xxx ESMTP
HELO 
[email protected]
250 ip-XX-XX-XXX-XXX.xxx.xxx.xxx
MAIL FROM:<
[email protected]>
250 ok
RCPT TO:<
[email protected]>
250 ok
DATA 
554 sorry, invalid mailbox name(s). (#5.1.1)
QUIT
I'm sure I missing something related 
to mailbox or alias creation, in fact I did nothing 
to define mailbox 
[email protected] anywhere. But I tried 
to search something on the net and on the numerous qmail man pages, bot I found nothing.