The user holds Global Jira Administrator permissions as well as the Role "Administrator". Still the user cant change any shemes of project (permission/notification schemes etc.).
A Jira system admin always has rights to change project schemes.
I'd say this person is probably not an admin, despite you thinking they are. Go to the user profile and look at the "groups" they are in. Then check the global permissions settings to check the admin groups. If in doubt, post the lists of groups they are in here, and the data on the global permissions screen.
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