OK. WIth 1.0.1 everything works as expected. (at least in terms of 
first login).

I think you can close this one.

OK. Just tested it in every detail.
This is what happens:

Extract from the relevant tables at the beginning:
MariaDB [horde]> select share_id,share_name,share_owner from 
kronolith_sharesng;
+----------+-------------------------+---------------+
| share_id | share_name              | share_owner   |
+----------+-------------------------+---------------+
|        1 | z9oXFQbcQUJNreta2pOGEeA | Administrator |
|       19 | GomeVwbcQUJNre0pdGsl9tA | <id1>          |
|       25 | NSPuBwbcQUJNre7pd8WWHyA | <id2>        |
|       28 | sk5hFQbcQUJNre9ZUEa2HzA | <id3>          |
+----------+-------------------------+---------------+
4 rows in set (0.00 sec)

MariaDB [horde]> select share_id, share_name, share_owner from nag_sharesng;
+----------+-------------------------+---------------+
| share_id | share_name              | share_owner   |
+----------+-------------------------+---------------+
|        1 | Y_oKbwbcQUJNretH0nn2DPA | Administrator |
|        6 | butdWgbcQUJNrewdN_lGizA | <id1>          |
|       15 | Tpd8TQbcQUJNre4onGFWEbA | <id2>        |
|       21 | UDYYDAbcQUJNre8JHW32EeA | <id3>          |
|       22 | LQNHNQbcQUJNre8JIaC19tA | <id3>          |
+----------+-------------------------+---------------+
5 rows in set (0.00 sec)

MariaDB [horde]> select share_id, share_name, share_owner from turba_sharesng;
+----------+-------------------------+---------------+
| share_id | share_name              | share_owner   |
+----------+-------------------------+---------------+
|        1 | GXzJFQbcQUJNres1vIEmEbA | Administrator |
|        6 | Cq9tZgbcQUJNrewczAiGizA | <id1>          |
|       15 | 3RliRAbcQUJNre4ocTRmEbA | <id2>        |
|       21 | d9QRHgbcQUJNre8I6N0V9tA | <id3>          |
|       22 | 7UF7awbcQUJNre8I9CKGEeA | <id3>          |
+----------+-------------------------+---------------+
5 rows in set (0.00 sec)




Now login as user "test" (id4):
In this case I get the above described behaviour:

Apr 19 23:56:36 <server> HORDE: HORDE [kronolith] PHP ERROR: Undefined 
index: 9AiOMwbcQUJNrgCCQ7zG86A [pid 29857 on line 1073 of 
"/srv/www/vhosts/<vhost-name>/htdocs_ssl/kronolith/lib/Kronolith.php"]
Apr 19 23:56:36 <server> HORDE: HORDE [kronolith] share parameter is 
missing [pid 29857 on line 33 of 
"/srv/www/vhosts/<vhost-name>/htdocs_ssl/kronolith/lib/Calendar/External/Tasks.php"]

Now disable kronolith, delete all cookies and login again:
root# mv conf.php conf.php_save
==> Login via Web (delete cookies first) as User "test" (<id4>):
< nothing happened till now in the database, so I don't post the 
content again >

... Logout... Now the entries nag_sharesng and turba_sharesng are created:

MariaDB [horde]> select share_id,share_name,share_owner from 
kronolith_sharesng;
+----------+-------------------------+---------------+
| share_id | share_name              | share_owner   |
+----------+-------------------------+---------------+
|        1 | z9oXFQbcQUJNreta2pOGEeA | Administrator |
|       19 | GomeVwbcQUJNre0pdGsl9tA | <id1>          |
|       25 | NSPuBwbcQUJNre7pd8WWHyA | <id2>        |
|       28 | sk5hFQbcQUJNre9ZUEa2HzA | <id3>          |
+----------+-------------------------+---------------+
4 rows in set (0.00 sec)

MariaDB [horde]> select share_id, share_name, share_owner from turba_sharesng;
+----------+-------------------------+---------------+
| share_id | share_name              | share_owner   |
+----------+-------------------------+---------------+
|        1 | GXzJFQbcQUJNres1vIEmEbA | Administrator |
|        6 | Cq9tZgbcQUJNrewczAiGizA | <id1>          |
|       15 | 3RliRAbcQUJNre4ocTRmEbA | <id2>        |
|       21 | d9QRHgbcQUJNre8I6N0V9tA | <id3>          |
|       22 | 7UF7awbcQUJNre8I9CKGEeA | <id3>          |
|       37 | 4zZtcwbcQUJNrgabftgXSpA | <id4>        |        <== This 
is the "test" acc.
+----------+-------------------------+---------------+
6 rows in set (0.00 sec)

MariaDB [horde]> select share_id, share_name, share_owner from nag_sharesng;
+----------+-------------------------+---------------+
| share_id | share_name              | share_owner   |
+----------+-------------------------+---------------+
|        1 | Y_oKbwbcQUJNretH0nn2DPA | Administrator |
|        6 | butdWgbcQUJNrewdN_lGizA | <id1>          |
|       15 | Tpd8TQbcQUJNre4onGFWEbA | <id2>        |
|       21 | UDYYDAbcQUJNre8JHW32EeA | <id3>          |
|       22 | LQNHNQbcQUJNre8JIaC19tA | <id3>          |
|       37 | MieuUwbcQUJNrgabq1J3SpA | <id4>        |       <=== This 
is the test account.
+----------+-------------------------+---------------+
6 rows in set (0.00 sec)

Last step: Reenable kronolith and login as user "test" again:
root# mv conf.php_save conf.php
==> Login via Web.
  ==> Everything works, but no new entries are created in 
kronolith_sharesng till now.
==> Logout

Now the last sharesng-entry is created:
MariaDB [horde]> select share_id,share_name,share_owner from 
kronolith_sharesng;
+----------+-------------------------+---------------+
| share_id | share_name              | share_owner   |
+----------+-------------------------+---------------+
|        1 | z9oXFQbcQUJNreta2pOGEeA | Administrator |
|       19 | GomeVwbcQUJNre0pdGsl9tA | <id1>          |
|       25 | NSPuBwbcQUJNre7pd8WWHyA | <id2>        |
|       28 | sk5hFQbcQUJNre9ZUEa2HzA | <id3>          |
|       33 | gqSPBAbcQUJNrghwBAg3azA | <id4>        |     <=== this is 
the test-account
+----------+-------------------------+---------------+
5 rows in set (0.00 sec)

From now on the user works.

This doesn't make any sense. If Kronolith is disabled, there are no 
entries created in kronolith_sharesng.

If a new user logs in (using IMP-IMAP-Authorisation) the User gets to 
the first screen, but the side-menu is empty.
As soon as he clicks on any icon visible the User gets an error saying:
"share parameter is missing"

You can avoid this by doing the following:
* "Disable" kronolith by moving conf.php to e.g. conf.php_save
* Login as the User
   ==> This creates the appropriate entries in kronolith_sharesng-table
* Reactivate kronolith (moving conf.php back to its original location)