Hi Sylvain,
Is possible that you have set the user to have the Customers view, that allow issues to be created but not managed.
To manage the issues using service desk, is important that this user is a Service desk manager.
Take a look here to see if the user has the proper permissions:
https://confluence.atlassian.com/display/SERVICEDESK/Setting+up+JIRA+Service+Desk+Users
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