Scheduled Issues after creation are private by default. Only the Creator and Jira Administrators can: edit, delete, share or manually execute Scheduled Issue. Manage Access option allows to grant execute, edit and delete permissions to each Scheduled Issue individually. Only the sharing permission (managing access) is kept for Creator and Jira Administrators
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To change Scheduled Issues access rights in bulk, please also access "Scheduled Issues" (1), tick ones of particular interest (2), press "Share Selected" (3).
For more information to actions, possible to perform in bulk, refer to this page.
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Use the drop-down menu cloaked under the "Projects" (1) to access a desired one and then go to the below located "Scheduled Issues" (2).
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If you want any of your users to be able to use TSP add-on, then you need to first grant him or her with an access via 
If sharing of an issue is fair enough, then the above-mentioned method is sufficient enough. In such case only sharing of a scheduled issue will be permitted without any possibility to amend it....