I configured successfully the external smtp server authentication following this guide: Outgoing SMTP Authentication - Zimbra :: Wiki.
There are several servers that need to be authenticate with the username of the account that is sending the mail. Then every user need to authenticate on external smtp server with its own username and password, different from other users, for example, gmail.com.
How can I do that? (Authenticate on an external smtp server with different username and password for every user, of the same domain or from different domains).