Note :  you must setup the email on outlook client first to set the permission of the public folder.

1. In the Folder List, in the Navigation Pane, right-click the public folder you want to share, and then click Properties on the shortcut menu.

You must have Owner permission for a public folder to set sharing permissions for the folder. You can set permissions for only one folder at a time.

2. Click the Permissions tab.
3. Click Add.
4. In the Search box, enter the name of the person you want to grant sharing permissions to.
5. Click Add, and then click OK.
6. In the Name list, click the name of the person you just added.
7. Under Permissions, choose the settings you want.

Note   You can assign everyone who has access to the folder the same permissions by clicking Default in the Name list.