I found errors: "You do not have sufficient privileges to send mail to this address. Please authenticate and try again."
in exim reject log

Code:
2018-03-19 15:31:35 H=mx6-out12.antispamcloud.com [95.211.*.*]:55952 X=TLSv1.2:ECDHE-RSA-AES256-GCM-SHA384:256 CV=no F=<> rejected RCPT <[email protected]>: You do not have sufficient privileges to send mail to this address.  Please authenticate and try again.
2018-03-19 15:54:14 H=proxy2.de [80.86.*.*]:55314 F=<[email protected]> rejected RCPT <[email protected]>: You do not have sufficient privileges to send mail to this address.  Please authenticate and try again.
The problem was that the hosting provider is using SPAM filtering system that require e-mail sender's mailbox to be able to accept e-mail.

On my WHM/cPanel server, i had all e-mails sent to system e-mail accounts (like [email protected]) rejected. In the Exim Configuration Manager > ACL Options; Check that you have not enabled:

Reject remote mail sent to the server's hostname

Reject mail at SMTP time if the recipient is an address of the primary hostname of this server. No remote mail should normally be received for the primary hostname, and this has recently become a common spam target.