In my environment, there is an Exhange 2007 server and an Exchange 2013 server. I have a few public folders in Exchange 2007 server. I want to know how a user in Exchange 2013 can access the public folders in Exchange 2007. I've searched for it a lot but could not come up with a working solution.
Public Folders changed dramatically in Exchange 2013, but coexistence of legacy public folders on older versions of Exchange (2007 and 2010) and Exchange 2013 is possible and supported. If you intend to keep the Exchange 2007 server around you can configure coexistence for legacy public folders. Outlook 2010 and 2013 clients will be able to access the public folders hosted by the Exchange 2007 server computer.
The summary of this legacy public folder coexistence is that Exchange 2013 has changed the way that Outlook clients are referred to Public Folder stores. There are some specific commands you can run, after you've applied Exchange 2013 Cumulative Update 5 (or later), to configure your environment for legacy public folder coexistence.
If you intend to disuse the Exchange 2007 server you should think about migration the folders to Exchange 2013. This process, which I think is rather ugly, involves and export/import of all the folders, and removal of the Exchange 2007 public folder configuration.