ok, in the original configuration this was set, but the array override 
killed it. So sorry about the confusion, some old examples led me to 
the override.

Because you haven't configured SMTP to use authentication.  See 
backends.conf (the smtp -> auth parameter).

Regardless, this is not a bug so this support discussion should move 
to the imp mailing list.

That's my config in backends.d:

<?php

$servers['imap']['disabled'] = true;
$servers['advanced']['disabled'] = false;
$servers['advanced']['hordeauth'] = true;
$servers['advanced']['name'] = 'Fakultät IMAP Server';
$servers['advanced']['hostspec'] = 'localhost';
$servers['advanced']['secure'] = 'none';
$servers['advanced']['admin']['params']['admin_user'] = '*******';
$servers['advanced']['admin']['params']['admin_password'] = '*******';
$servers['advanced']['admin']['params']['userhierarchy'] = 'user/';
$servers['advanced']['smtp']['debug'] = '/tmp/smtp.log';
$servers['advanced']['smtp']['host'] = 'mail.physik.uni-muenchen.de';
$servers['advanced']['smtp']['port'] = 587;
$servers['advanced']['quota']['params']['unit'] = 'GB';
$servers['advanced']['cache'] = 'none';
$servers['advanced']['maildomain'] = 'physik.uni-muenchen.de';

As you can see $servers['advanced']['hordeauth'] = true; is set. And 
it does not work, are you sure the configuration at your site really 
works the way you want? See the smtp.log:

------------------------------
S: 220 mail.physik.uni-muenchen.de ESMTP Postfix
C: EHLO testwebmail.physik.uni-muenchen.de
S: 250-mail.physik.uni-muenchen.de
S: 250-PIPELINING
S: 250-SIZE 31457280
S: 250-VRFY
S: 250-ETRN
S: 250-STARTTLS
S: 250-XVERP
S: 250-ENHANCEDSTATUSCODES
S: 250-8BITMIME
S: 250 DSN
C: STARTTLS
S: 220 2.0.0 Ready to start TLS
C: EHLO testwebmail.physik.uni-muenchen.de
S: 250-mail.physik.uni-muenchen.de
S: 250-PIPELINING
S: 250-SIZE 31457280
S: 250-VRFY
S: 250-ETRN
S: 250-AUTH LOGIN PLAIN
S: 250-AUTH=LOGIN PLAIN
S: 250-XVERP
S: 250-ENHANCEDSTATUSCODES
S: 250-8BITMIME
S: 250 DSN
C: MAIL FROM:<Campus-admin@physik.uni-muenchen.de> SIZE=593 BODY=7BIT
C: RCPT TO:<Klaus.Steinberger@physik.uni-muenchen.de>
S: 250 2.1.0 Ok
S: 554 5.7.1 
<testwebmail.physik.uni-muenchen.de[2001:4ca0:4102::2:200]>: Client 
host rejected: Access denied
C: RSET
S: 250 2.0.0 Ok
C: QUIT
S: 221 2.0.0 Bye


As you can see authentication is never tried.

I did and as I told you, it works for me. But in the above contents of 
the imp/config/backends.local.php one line was missing. These are the 
full contents of this file on my system:

<?php
$servers['imap']['disabled'] = true;

$servers['advanced']['disabled'] = false;
$servers['advanced']['hordeauth'] = true;
$servers['advanced']['maildomain'] = 'de-korte.org';
$servers['advanced']['cache'] = 'sql';
$servers['advanced']['quota']['params']['unit'] = 'GB';
$servers['advanced']['quota']['params']['hide_when_unlimited'] = false;
$servers['advanced']['spam']['innocent']['program'] = '/usr/bin/spamc 
-C revoke';
$servers['advanced']['spam']['innocent']['display'] = true;
$servers['advanced']['spam']['spam']['program'] = '/usr/bin/spamc -C report';
$servers['advanced']['spam']['spam']['display'] = true;
$servers['advanced']['autocreate_special'] = true;

You may run into problems if the second line is missing, since then 
Horde will use the 'imap' configuration, instead of the 'advanced' 
configuration. The only other thing that would need an override in 
your case, is

$servers['advanced']['smtp']['host'] = 'mail.physik.uni-muenchen.de';
I don't use a dedicated account for SMPT AUTH, the credentials that 
users entered when logging into the Horde portal are used. I'm 100% 
sure this works, since the SMTP FROM address is checked to verify that 
a user is allowed to use a sender address (to prevent them from 
spoofing addresses).

Because it is IMP specific.

Horde authentication credentials are set in Horde_Core_Factory_Mail.   
Note that username_auth and password_auth horde config values need to 
be active (non-empty).

Some more debugging:

I added some debug output, as well as changed line 440/441 to respect 
the horde_auth parameter, so the code tries authentication:

Connection to: smtp://mail.physik.uni-muenchen.de:587
S: 220 mail.physik.uni-muenchen.de ESMTP Postfix
C: EHLO testwebmail.physik.uni-muenchen.de
S: 250-mail.physik.uni-muenchen.de
S: 250-PIPELINING
S: 250-SIZE 31457280
S: 250-VRFY
S: 250-ETRN
S: 250-STARTTLS
S: 250-XVERP
S: 250-ENHANCEDSTATUSCODES
S: 250-8BITMIME
S: 250 DSN
C: STARTTLS
S: 220 2.0.0 Ready to start TLS
C: EHLO testwebmail.physik.uni-muenchen.de
S: 250-mail.physik.uni-muenchen.de
S: 250-PIPELINING
S: 250-SIZE 31457280
S: 250-VRFY
S: 250-ETRN
S: 250-AUTH LOGIN PLAIN
S: 250-AUTH=LOGIN PLAIN
S: 250-XVERP
S: 250-ENHANCEDSTATUSCODES
S: 250-8BITMIME
S: 250 DSN
C: AUTH LOGIN
S: 334 VXNlcm5hbWU6
C:
S: 334 UGFzc3dvcmQ6
[AUTH Command - method: LOGIN; username: ]
S: 535 5.7.8 Error: authentication failed: generic failure
[AUTH Command - method: PLAIN; username: ]
S: 535 5.7.8 Error: authentication failed: generic failure
C: QUIT
S: 221 2.0.0 Bye
quit

As you can see the code never gets the correct credentials. This is 
due to the fact that in Line 776 in /usr/share/pear/Horde/smtp.php in 
the function _auth username and password will be filled with the 
parameters username and password, which resembled a dedicated login 
for SMTP delivery.

But what we need is the login credentials of the user!

It is indeed in a file in backends.d
ok, i changed that.
No, definitly not, I _need_  horde_auth as my SMTP server requires 
authentication with the user credentials, and this part is missing in 
the code. Did you not read my comments correctly?
That only works if the SMTP servers needs no authentication or works 
with an dedicated account!

Jan:  please do not mark it as no bug so fast!

I it as regression in the code.

Don't modify imp/config/backends.php. Ever. See the comments in the header.
Don't override arrays, only the values of individual elements:

<?php
$servers['advanced']['disabled'] = false;
$servers['advanced']['hordeauth'] = true;
$servers['advanced']['smtp']['debug']  = '/tmp/smtp.log';
$servers['advanced']['smtp']['host'] = 'mail.physik.uni-muenchen.de';

should be sufficient (and works for me).
  As far as I know, the horde_auth parameter is no longer used. I use 
the above configuration without overriding *any* 'smtp' value.

these in config backends.php:

$servers['advanced']['smtp'] = array(
                 'auth' => true,
                 'horde_auth' => true,
                 'debug' => '/tmp/smtp.log',
                 'host' => 'mail.physik.uni-muenchen.de',
                 'port' => 587,
         );

horde_auth is not used anywhere in Horde_smtp (but it worked before 
the change to Horde_SMTP), look into /usr/share/pear/Horde/Smtp.php at 
line 440/441, the code looks only for "username" which is for 
authentication with _one_ fixed account. We need to use horde_auth, so 
that the credentials of the user are used.

I did change these two lines, but later in the code also horde_auth is 
not used.

What parameter are you talking about?

After upgrading to horde 5.2.1 we were not able to send emails using 
horde_auth authentication.
Some investigating in the code shows that Horde_SMTP does not use the 
horde_auth Parameter.

This is important functionality for us, which got lost with the change 
from Net_SMTP to Horde_SMTP

Please reintroduce this functionality