The following problem replicates with Exchange 2010 SP1 and the two types of mobile devices here: iPhone with iOS 6.1.2 and Windows Phone 7.5 ...
Using Outlook, a mail item is moved from the Inbox to a Public Folder.
The mail item stays listed in the mobile device's Inbox.
The workaround is to copy the mail item from the Inbox on Outlook, then delete the item from the Outlook Inbox ... this works but is inconvenient.
Any suggestions? Thank you.