Marc is right but it is not my case. We have a commercial Internet link. I could bypass the ISP if the mail server was under my control, which is not the case.

This is why my first guest with Zimbra was to leave the account management and POP/Imap services to my current mail supplier, and just get a backup SMTP, authenticating with the recipient domain, since no account exist on the zimbra server. But Marc convince me that this is not, or not easily doable so I will eventually merge all the system to a local Zimbra.