[Pkg-exim4-users] exim4 won't listen anyone from outside but telnet

[Igor Bogomazov]

Hello exim4 users/developers,

I have installed exim4 as 'internet'-server and learnt
to do several great things: to send emails anywhere
(and to any local user as well), to check and download
emails from server (using dovecot indeed), also I've
tuned up TLS and made exim4 to listen to the 465 port.

The only thing I want else is to be able to receive emails
from another servers. But they won't do with an error:
{
Google tried to deliver your message, but it was rejected by the
recipient domain.
We recommend contacting the other email provider for further information
about the cause of this error.
The error that the other server returned was: 550 550-5.1.1 The email
account that you tried to reach does not exist.
Please 550-5.1.1 try double-checking the recipient's email address for
typos 550-5.1.1 or unnecessary spaces.
}

The same error gives not only Google.
Though I've tried to "telnet 25" and compose a simple letter
by hands, and it has been done!
I think telnet is not the proper way to send emails,
so I need your help.

Thanks for any help!
Igor