exim4 on debian 7.8 sent mail never arrives @gmail

I followed the instruction on this page Debian Exim and configured my exim with a single file via the dpkg-reconfigure exim4-config setup.

Now I can send mails between local users (from root to myuser or from webmaster to myuser). Additionally I can receive mails from my googlemail.com account.

But when I'm sending mail to this googlemail account it never says hello to my inbox :-(.

In the /var/log/exim4/mainlog I see the following:

2015-02-26 15:51:25 1YQzmf-0000sP-W3 <= myuser@myserver.domain.com U=myuser P=local S=587
2015-02-26 15:51:27 1YQzmf-0000sP-W3 => account@googlemail.com R=dnslookup T=remote_smtp H=gmail-smtp-in.l.google.com [2a00:1450:4013:c01::1a] X=TLS1.2:RSA_ARCFOUR_SHA1:128 DN="C=US,ST=California,L=Mountain View,O=Google Inc,CN=mx.google.com"
2015-02-26 15:51:27 1YQzmf-0000sP-W3 Completed

I searched for hours on Google, but can't figure out what causes this problem..

Any suggestions or information you may need to give me hints on what I have to do are very welcome!