By default, organization members have write access to their organization's project boards unless organization owners or project board admins set different permissions for specific project boards.
Setting a baseline permission level for all organization members
Tip: You can give an organization member higher permissions to project board. For more information, see "Project board permissions for an organization."
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In the upper-right corner of GitHub Enterprise Server, select your profile photo, then click Your organizations.  
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Click the name of your organization. 
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Under your organization name, click Projects. 
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In the projects list, click the name of the project board. 
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On the top-right side of the project board, click Menu. 
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Click , then click Settings.  
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Under "Organization member permission", choose a baseline permission level for all organization members: Read, Write, Admin, or None. 
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Click Save.