Exchange migrated, ActiveSync not working as supposed

After a complete Exchange 2013 migration, everything works, but some users are complaining, that their mobile devices are not being updated with e-mails anymore.

You try to delete their account and add it again, all is good when doing that, but the Inbox stays empty!

This is mostly common to the Active Directory permissions, not being inherited on the users object, so try this (On server 2012 R2, but looks almost the same on 2008 R2):

Go into your user account in AD Users and Computers. (Make sure you have Advanced Features checked in the View menu.)  Go to the Security tab, Advanced and select “Enable Inheritance” answer they question and click OK. Retry your ActiveSync right away.