I got the solution ! I've compared the email headers of one email sent from the LAN and one email sent from the webmail : - in the first case, the oldest "received from" is 127.0.0.1 and the public IP address - in the 2nd case, the oldest "received from" header is the name of the web mail component which is also indicated in the X-mailer header, and the public IP address is indicated in another "received from" header.
Thanks again Senjai for your precious help that put a little on the way !