To check permissions you can use JIRA Permission Helper

User "Recurring Tasks for JIRA" is a member of project role "atlassian-addons-project-access" (or other project role, depends on your current configuration)

You can create separate project role ("gebsun-addons-project-access") to harden security and use the role to grant following permissions for "Recurring Tasks for JIRA" plugin.
Project role "atlassian-addons-project-access" (or other project role) need to have CREATE ISSUE following permissions
How to add permissions:
1. Go to JIRA Administraton->Projects
2. Click on selected project
3. Select "Permissions"
4. "Click in upper right corner "Edit permissions"
5. Click "Edit" link on "Create Issue" row
6. Add "Create Issue" permission for "atlassian-addons-project-access" (or other project role defined)

If you want to read more about administering JIRA permissions follow: Configuring Security

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