Hello,

We are in the middle of planning a cross forest migration from Exchange 2010 to Exchange 2013. 

To give some context:

We already have an Exchange 2013 environment complete with mailboxes, and public folders etc. We have a 2010 Exchange server in a different forest that we would like to migrate all existing mailboxes and public folders from to the Exchange 2013 forest. We will be keeping the domain/forest that currently contains 2010 so all mailboxes that will be moved will end up being linked mailboxes in the 2013 organization with the accounts held in the other forest. 

One of the big unanswered questions remains around public folder access. During migration there will be a time when some users will be in the Exchange 2010 organization, and some will be in the Exchange 2013 organization. I have two main questions around this

1. Is there any way possible that anyone can think of that the users moved to 2013 can access the public folders still on 2010?
2. What is the best way to migrate the public folders over from 2010 to 2013? Do we have to create the public folders and permissions on 2013 before hand or do we use a 3rd party tool or other method to achieve this goal?

Based on your mentioned description, I would refer you on below mentioned article that covers all the required aspects while need to migrate public folders from Exchange 2010 to 2013 : http://exchangeserverpro.com/exchange-server-2010-2013-migration-moving-public-folders/

One more informative resource can be explored here : http://www.msexchange.org/articles-tutorials/exchange-server-2013/migration-deployment/migrating-public-folders-exchange-2013-part1.html

If you wish to accomplish this job using third party, you may consider on LepideMigrator for Exchange tool that provides a very hassle-free environment to get this job done in an easier way without having any interruption.

Hi,

To reduce needless trouble, I recommend migrate mailbox first and public folder second.

However, public folder will works fine no matter where it located. If you experience an issue about user in Exchange 2013 mailbox cannot access Public Folder in Exchange 2010, please change the RPC authentication to NTML.
More details about it, please refer to: https://social.technet.microsoft.com/Forums/exchange/en-US/3172435f-4c06-41b3-b7a7-937dc0160049/exchange-2013-users-unable-to-access-exchange-2007-public-folders?forum=exchangesvrdeploy

Additional, step by step to migrate Public folder to Exchange 2013, for your reference:
http://blogs.technet.com/b/meamcs/archive/2013/07/25/part-4-step-by-step-exchange-2007-to-2013-migration.aspx

Thanks