If you will be receiving email via Google mail and have a custom domain registered with them e.g. yourdomain.com, but that domain is also pointing to your server then you need to setup a hubbed host on your server to properly receive mail sent from your server at smth@yourdomain.com. The server (exim) needs to know that “smth” is not a user on the server but a email inbox at Google.

cat /etc/exim4/conf.d/router/150_exim4-config_hubbed_hosts

# router/150_exim4-config_hubbed_hosts
#################################

# route specific domains manually.
#
# see exim4-config_files(5) and spec.txt chapter 20.3 through 20.7 for
# more detailed documentation.

hubbed_hosts:
  debug_print = "R: hubbed_hosts for $domain"
  driver = manualroute
  domains = "${if exists{CONFDIR/hubbed_hosts}\
                   {partial-lsearch;CONFDIR/hubbed_hosts}\
              fail}"
  same_domain_copy_routing = yes
  route_data = ${lookup{$domain}partial-lsearch{CONFDIR/hubbed_hosts}}
  transport = remote_smtp

vi /etc/exim4/hubbed_hosts

It should contain this:

yourdomain.com: mx.external.com:aspmx.l.google.com

systemctl restart exim4

Before:

root@yourdomain # exim -bt smth@yourdomain.com
R: system_aliases for smth@yourdomain.com
smth@yourdomain.com is undeliverable: Unrouteable address

After:

root@yourdomain # exim -bt smth@yourdomain.com
R: hubbed_hosts for yourdomain.com
smth@yourdomain.com
router = hubbed_hosts, transport = remote_smtp
host aspmx.l.google.com      [2a00:1450:400c:c0b::1b]
host aspmx.l.google.com      [74.125.140.27]         
host alt1.aspmx.l.google.com [2a00:1450:4010:c0f::1b]
host alt1.aspmx.l.google.com [108.177.14.27]         
host alt2.aspmx.l.google.com [2404:6800:4003:c00::1a]
host alt2.aspmx.l.google.com [74.125.200.27]         
host aspmx2.googlemail.com   [2a00:1450:4010:c0f::1a]
host aspmx2.googlemail.com   [108.177.14.27]         
host aspmx3.googlemail.com   [2404:6800:4003:c00::1b]
host aspmx3.googlemail.com   [74.125.200.26]

• Debian 9

• manual: man exim4-config_files
• http://www.yann.com/en/configure-exim4-to-bypass-local-delivery-on-web-server-17/04/2014.html