you are right! thanks for that great support.

The client uses the ORGANIZER property to determine if the user is the 
event owner. The user email is a part of this property, so for this to 
work, both the email address you put in your identity pref in horde 
and the email the client was configured with MUST match.

I do only have an user name in horde no e-mail functionality. On the 
smartphone I entered "user@serveraddress"

It sounds like you might have configured your client with a different 
email address then the one horde knows you as.

I sync all my calendar entries over activesync.

If I create an appointment in Kronolith I see only an invitation on 
the smartphone. The appointment itself cannot be changed on the 
device. But backwards, it works (create appointment on smartphone -> 
sync to horde)