I did; still same problem
To sum up here is the following problem:
SEND MAIL: (no problem here) I click on "Send mails"; mails are send to the Local Postfix server which uses the Internet mail server as relay to send the mail to its destination.
RECEIVE MAIL: (less funny for me) I get a new mail modified by the Internet mail server (see below); it is retrieved and stored on a local mailboxe by and on the local server (thanks to the godly powers of fetchmail and Cyrus).
But, the fetchmail foul beast system keeps retrieving mails modified by the Internet mail server at each poll, even if it has been read or whatever; to get rid of that mail I need to manually delete it on the Internet mail server.
When I dumbly and stubbornly click the "retrieve mail" button of OE, I get more and more copies of the same mail, because of fetchmail.
Type of mails not liked by Fetchmail:
Whenever a mail is modified or returned by the Internet mail server, fetchmail keeps downloading it at each row; here some example.
1/-----------------------------------------
From: MAILER-DAEMON@internet_mail_server
To: User X
Topic: Failure notice
Hi. This is the qmail-send program at Internet_mail_server.
I'm afraid I wasn't able to deliver your message to the following addresses.
This is a permanent error; I've given up. Sorry it didn't work out.
<user_mail_adress>:
IP_Address does not like recipient.
Remote host said: 550 user unknown
Giving up on IP_Address
--- Below this line is a copy of the message
(Insert original message here)
2/-----------------------------------------
From: Insert_evil_spammer_name_here
To: Innocent_user
Topic: Fw: *** SPAM ALERT *** Spam mail title
----- Original Message -----
(Insert wonderful spam here)
Thanks for your replies 
