mail
 

I use Postfix, fetchmail, imap
I have no procmail
Every sent mail (including the mails which are sent to local users) goes out to the internet through the relayhost.
For example I send two mais:

localuser@mydomain -> to local user
remote@hotmail.com -> to remote user in the internet

Both the mails goes out to the internet through the relayhost.
The problem is that the localuser doesn't get his mail.

How does mailserver know which mail is sent to local user and which mail is sent to the remote address?

Take a look at this section of the postfix documentation:
http://www.postfix.org/BASIC_CONFIGU...#mydestination