Setting up exim. Why is mail not being received?

Question

PHP

Colleagues, welcome!
Please help me figure out the problem, or rather, my curvature) I'm
setting up exim4 for the first time and ran into a problem.
There is a VPS with Ubuntu 14.04. Set up nginx + php-fpm. The site on opencart is spinning on the server.
I'm setting up exim4 to notify about orders. And I ran into the following problem.
When creating an order by mail to the admin (mail to gmail), the order falls, and the notification of the order does not fall to the buyer (mail to rambler and yandex).
Exim log on the example of one order

2015-09-19 00:32:38 1Zd3Go-0001AE-3Z <= [email protected] U=www-data P=local S=8911
2015-09-19 00:32:38 1Zd3Go-0001AL-4q <= <> R=1Zd3Go-0001AI-4P U=Debian-exim P=local S=1862
2015-09-19 00:32:38 1Zd3Go-0001AL-4q => www-data R=local_user T=mail_spool
2015- 09-19 00:32:38 1Zd3Go-0001AL-4q Completed
2015-09-19 00:32:38 1Zd3Go-0001AP-5f <= [email protected] U=www-data P=local S=1347
2015 -09-19 00:32:38 1Zd3Go-0001AP-5f => [email protected] R=dnslookup T=remote_smtp H=gmail-smtp-in.l.google.com [74.125.205.26] X=TLS1.2 :RSA_ARCFOUR_SHA1:128 DN="C=US,ST=California,L=Mountain View,O=Google Inc,CN=mx.google.com" C="250 2.0.0 OK 1442611958 l9si7687722lae.99 - gsmtp"
2015- 09-19 00:32:38 1Zd3Go-0001AP-5f Completed
2015-09-19 00:32:48 1Zd3Go-0001AE-3Z ** [email protected] R=dnslookup T=remote_smtp: SMTP error from remote mail server after RCPT TO:: host imx1.rambler.ru [81.19.66.235 ]: 554 5.7.1 Helo command rejected
2015-09-19 00:32:48 1Zd3Gy-0001AZ-AG <= <> R=1Zd3Go-0001AE-3Z U=Debian-exim P=local S=9823
2015-09- 19 00:32:48 1Zd3Go-0001AE-3Z Completed
2015-09-19 00:32:48 1Zd3Gy-0001AZ-AG => www-data R=local_user T=mail_spool
2015-09-19 00:32:48 1Zd3Gy- 0001AZ-AG Completed

Judging by the log, when sending a notification to the admin, the sender appears [email protected], but gmail receives a letter from the [email protected] mailbox specified in opencart.
Tell me which way to set up.

Answer 1

Pay attention to
Specify what you are giving away as HELO/EHLO