Since SP1 for Exchange 2013 it could be possible, that just mail-enabling a Public Folder isn’t enough to make this Folder receiving external Mails. This is caused by a missing permission for external Senders (which appear as “Anonymous”) to “create” items in this specific folder.
If you track an external message, you may receive the following error:
RecipientStatus: {[{LRT=};{LED=550 5.7.1 RESOLVER.RST.AuthRequired; authentication required [Stage: CreateMessage]};{FQDN=};{IP=}]}
To resolve this issue, you have to drop the following command within the Exchange Management Shell:
Add-PublicFolderClientPermission –identity “\Folder\Subfolder” –User Anonymous –AccessRights CreateItems
This should resolve your problem.