Hi - mit dem Port 587 und FQDN (smtp.1und1.de:587) scheint es zu gehen 
Hier das eingestellte (Temp)Setup:
postconf relayhost=smtp.1und1.de:587
nano /etc/postfix/smtp_auth
--> smtp.1und1.de:587 ACCOUNT@MEINE-DOMAIN.de:KENNWORT
postmap /etc/postfix/smtp_auth
postfix reload
Und hier den Eintrag aus dem Log:
Feb 26 19:13:52 ucs3 postfix/postfix-script[14405]: refreshing the Postfix mail system
Feb 26 19:13:52 ucs3 postfix/master[2264]: reload -- version 2.11.3, configuration /etc/postfix
Feb 26 19:15:41 ucs3 postfix/smtpd[15599]: connect from localhost[127.0.0.1]
Feb 26 19:15:41 ucs3 postfix/smtpd[15599]: D6ACE507F7D: client=localhost[127.0.0.1]
Feb 26 19:15:41 ucs3 postfix/cleanup[15604]: D6ACE507F7D: message-id=<kcim.5a944ecd.3cea.4d4af64c56102b45@ucs3.MEINE-DOMAIN.local>
Feb 26 19:15:41 ucs3 postfix/qmgr[14409]: D6ACE507F7D: from=<ACCOUNT@MEINE-DOMAIN.de>, size=1973, nrcpt=2 (queue active)
Feb 26 19:15:41 ucs3 postfix/smtpd[15599]: disconnect from localhost[127.0.0.1]
Feb 26 19:15:42 ucs3 postfix/smtpd[15612]: connect from localhost[127.0.0.1]
Feb 26 19:15:42 ucs3 postfix/smtpd[15612]: 4D809507FC5: client=localhost[127.0.0.1], orig_queue_id=D6ACE507F7D, orig_client=localhost[127.0.0.1]
Feb 26 19:15:42 ucs3 postfix/cleanup[15604]: 4D809507FC5: message-id=<kcim.5a944ecd.3cea.4d4af64c56102b45@ucs3.MEINE-DOMAIN.local>
Feb 26 19:15:42 ucs3 postfix/qmgr[14409]: 4D809507FC5: from=<ACCOUNT@MEINE-DOMAIN.de>, size=2741, nrcpt=1 (queue active)
Feb 26 19:15:42 ucs3 postfix/smtpd[15612]: 514FF507FC6: client=localhost[127.0.0.1], orig_queue_id=D6ACE507F7D, orig_client=localhost[127.0.0.1]
Feb 26 19:15:42 ucs3 postfix/cleanup[15604]: 514FF507FC6: message-id=<kcim.5a944ecd.3cea.4d4af64c56102b45@ucs3.MEINE-DOMAIN.local>
Feb 26 19:15:42 ucs3 postfix/qmgr[14409]: 514FF507FC6: from=<ACCOUNT@MEINE-DOMAIN.de>, size=2442, nrcpt=1 (queue active)
Feb 26 19:15:42 ucs3 amavis[20988]: (20988-01) Passed CLEAN {RelayedInternal,RelayedOutbound}, LOCAL [127.0.0.1]:44680 <ACCOUNT@MEINE-DOMAIN.de> -> <emailbackups@MEINE-DOMAIN.local>,<ACCOUNT@TEST-DOMAIN.de>, Queue-ID: D6ACE507F7D, Message-ID: <kcim.5a944ecd.3cea.4d4af64c56102b45@ucs3.MEINE-DOMAIN.local>, mail_id: loSx4hsP-0Ue, Hits: 1.517, size: 1973, queued_as: 4D809507FC5/514FF507FC6, 423 ms
Feb 26 19:15:42 ucs3 postfix/smtp[15605]: D6ACE507F7D: to=<emailbackups@MEINE-DOMAIN.local>, relay=127.0.0.1[127.0.0.1]:10024, delay=0.49, delays=0.05/0.02/0.01/0.42, dsn=2.0.0, status=sent (250 2.0.0 from MTA(smtp:[127.0.0.1]:10025): 250 2.0.0 Ok: queued as 4D809507FC5)
Feb 26 19:15:42 ucs3 postfix/smtp[15605]: D6ACE507F7D: to=<ACCOUNT@TEST-DOMAIN>, relay=127.0.0.1[127.0.0.1]:10024, delay=0.49, delays=0.05/0.02/0.01/0.42, dsn=2.0.0, status=sent (250 2.0.0 from MTA(smtp:[127.0.0.1]:10025): 250 2.0.0 Ok: queued as 4D809507FC5)
Feb 26 19:15:42 ucs3 postfix/qmgr[14409]: D6ACE507F7D: removed
Feb 26 19:15:42 ucs3 postfix/lmtp[15613]: 4D809507FC5: to=<emailbackups@MEINE-DOMAIN.local>, relay=127.0.0.1[127.0.0.1]:2003, delay=0.2, delays=0.02/0.01/0.03/0.15, dsn=2.1.5, status=sent (250 2.1.5 emailbackups@MEINE-DOMAIN.local Ok)
Feb 26 19:15:42 ucs3 postfix/qmgr[14409]: 4D809507FC5: removed
Feb 26 19:15:42 ucs3 postfix/smtp[15615]: 514FF507FC6: to=<ACCOUNT@TEST-DOMAIN>, relay=smtp.1und1.de[212.227.15.167]:587, delay=0.65, delays=0.01/0.03/0.38/0.23, dsn=2.0.0, status=sent (250 Requested mail action okay, completed: id=0LcrJc-1eQ9FO3XLU-00iCPf)
Feb 26 19:15:43 ucs3 postfix/qmgr[14409]: 514FF507FC6: removed
So werde jetzt noch die Konfig im Original-Setup anpassen und das System neu starten.
Bis dann