When the user uses Outlook, the AutoDiscover response for their mailbox will include a publicFolder value that contains this email address given to the users mailbox. Once this is done, all Exchange Online users get allocated one of these email addresses as their public folder proxy address. For example this would look like Set-OrganizationConfiguration -PublicFoldersEnabled Remote -RemotePublicFolderMailboxes pfProxy1. This is done with Set-OrganizationConfiguration in Exchange Online and the value is the email address(es) of mailboxes that are located on the same servers as the public folder servers on premises – these are known as the public folder proxy mailboxes. When you set up integration between Exchange Online and an on-premises Exchange organization, you choose the single organization that you can proxy public folder requests to. In multi-forest hybrid you will have users from more than one forest (of course). That is easy for hybrid mode Exchange Server to Exchange Online, but once you move to multi-forest hybrid it is not. The specifics of the scenario is that with Exchange Online mailboxes and on-premises public folders, each user in Exchange Online needs a login account in the on-premises forest. The original info below remains as the principle of the information is fine to read and understand – but the specifics of the implementation have changed: Please scroll down to bottom for the specific changes that are added to this post. Update: March 2018 – this process below has changed considerably due to changes in the Exchange Online and AutoDiscover that have stopped this process working for random subsets of customers. But it does allow some very specific problems with public folder integration to be solved in the short term. This is not something that I recommend implementing lightly, as there are implications. Here is a scenario I have come across in a few clients in just the last few weeks. Now rather than the below post from me, you can set a users mailbox to see public folders or not as required and then enable the global setting to turn on controlled access to public folders.

Microsoft have added support to hide public folders in Exchange Online.

What can exchange public folder do