Although you can manage permissions in Exchange Management Shell, in ecp when you click on Manage Permissions on specific folder the following page is shown:

500 Unexpected Error

To resolve this issue:

1. Use PowerShell to check Public Folder Client Permissions:
PS > Get-PublicFolderClientPermission \FolderName |Format-List

2. Check if any user has a SID instead of a username

3. Remove users with SID if any:
PS > Remove-PublicFolderClientPermission -Identity \FolderName -User NT:S-1-1-11-11111111-1111111111111-1111

4. Check if you can manage Public Folder permissions via ecp