No permissions for incident update over REST-API when ticket closed

Case1: If I am logged into the system via GUI, I can update a ticket that is already closed

Case2: If is the same about REST I try to get an error:
HTTP Response Content: {“errorMessages”:[“You do not have permission to edit issues in this project.”],“errors”:{}}

The username is identical in both cases.
Please help. What can I do?

Additional Info:
I can update via API closed issue with type Bug. But the closed issue with type customize not. Why?