So, I configured... stuff... at the moment I cannot tell you, what exactely I did, but I produced this log entry:
May 25 20:53:42 myserver sendmail[9261]: NOQUEUE: connect from localhost [127.0.0.1]
May 25 20:53:42 myserver sendmail[9261]: AUTH: available mech=ANONYMOUS CRAM-MD5 DIGEST-MD5 LOGIN PLAIN, allowed mech=EXTERNAL GSSAPI KERBEROS_V4 DIGEST-MD5 CRAM-MD5 PLAIN LOGIN
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: Milter: no active filter
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 220 myserver.mydomain ESMTP Sendmail 8.13.6/8.13.6/SuSE Linux 0.8; Fri, 25 May 2007 20:53:42 +0200
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: <-- EHLO myserver.mydomain
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-myserver.mydomain Hello localhost [127.0.0.1], pleased to meet you
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-ENHANCEDSTATUSCODES
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-PIPELINING
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-8BITMIME
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-SIZE
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-DSN
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-ETRN
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-AUTH DIGEST-MD5 CRAM-MD5 PLAIN LOGIN
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250-DELIVERBY
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250 HELP
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: <-- MAIL FROM: <Me@MyDomain.com> RET=HDRS ENVID=H000006a00000b3b.1180119221.myserver.mydomain
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: ldap
Me@MyDomain.com => s04
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250 2.1.0 <Me@MyDomain.com>... Sender ok
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: <-- RCPT TO: <recipient@googlemail.com> NOTIFY=DELAY,FAILURE
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250 2.1.5 <recipient@googlemail.com>... Recipient ok
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: <-- DATA
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 354 Enter mail, end with "." on a line by itself
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: from=<Me@MyDomain.com>, size=869, class=0, nrcpts=1, msgid=<H000006a00000b3b.1180119221.s04.umn@MHS>, proto=ESMTP, daemon=Daemon0, relay=localhost [127.0.0.1]
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8k009261: --- 250 2.0.0 l4PIrg8k009261 Message accepted for delivery
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8l009261: <-- QUIT
May 25 20:53:42 myserver sendmail[9261]: l4PIrg8l009261: --- 221 2.0.0 s04.umn closing connection
May 25 20:53:42 myserver sendmail[9289]: l4PIrg8k009261: ldap
Me@MyDomain.com => s04
May 25 20:53:42 myserver sendmail[9289]: l4PIrg8k009261: to=<recipient@googlemail.com>, delay=00:00:00, xdelay=00:00:00, mailer=relay, pri=120869, relay=my.external.smtp.server., dsn=4.0.0, stat=Deferred
Probably somebody could tell me what's not working - the emails are not going out anymore.