The configuration page for Service Desk Reporter is located under Administration >> Add-ons >> Service Desk Reporter Settings.
Through this page you can select the user groups that have access to Service Desk Reports and separately you can select the user groups that are allowed to export the complete report data as Excel.
Performance note
Excel export on large datasets can start an expensive calculation on the server and may have a performance cost. So export permission is separated from report access permission to allow admins limit the group of people that can export data.
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