Hi Bharath, thanks for the answer.
User has access to LCM and content there is split into folders. So view on LCM and full controll on folder containing promote job.
I've tried to use both - LDAP and Enterprise accounts.
details about my main problem, but as I've mentioned I've sent incident to SAP about this problem, but no working resolution yet found:
In promotion management no error occures, there is no sign that promotion management job was tried to be execute. Status is not being changed (if it was created, that it stays created, no failure or success status). Last run date is also not being updated.
Afterwards I've found, that administrator can see failed promotion job in Instance Manager with error:
Object failed to run due to an error while processing on the Job Server.