ANSWER: I entered in the various mail clients directly to the ip of the mail servers of the provider and the client as I entered the dns server ip dns procedure. So the login is immediate without errors applicazone local policy in the event log and the mail is working properly.
MORAL: Never use an extension for public local domains (. Com,. Com, etc.) but always use the extension. Or similar premises in order to avoid these unpleasant drawbacks.