Login to Exchange Server
Open Exchange Management Console
Click On Toolbox (Tree Item)
Select Public Folder Management Console on the Toolbox window
Click on Default Public Folder
Note: It takes some time to synchronize content, depending on the server
Select the folder and go to properties -> Go to permissions (tab)
Add the user, define the permission level
Note: Please make sure the permission are defined at the item level
Reference
https://www.youtube.com/watch?v=uMjZ5UsVALs