In general, two types of accounts can manage Exchange Server public folder permissions: Exchange Administrators and Public Folder Owners. Because you are missing the Owner for the Exchange public folder, it is not possible to manage the public folder's permissions from Microsoft Outlook.
Someone with Exchange Administrator or Exchange Full Administrator rights can still manage the public folder permissions using the Exchange System Manager (ESM), so you should be able to use it to control the permissions as long as you are logged on as an account with the appropriate Exchange Administrator role. However, Exchange public folder permissions are quite complex and that still might not solve the problem.
For more help, read Microsoft's article, Unable to set client permissions on Exchange public folders through Exchange System Manager.
If that still doesn't do the trick, you may need to dig deeper into the Exchange public folder permission model. A good reference is the TechNet article, Working with Exchange public folder and mailbox permissions.
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