Shared Mailbox - Users unable to rename folders

Hello !

I have a little(big) problem. I've searched a forum, read a lot of topics but couldn't find a right solution for my case.

So... there is a shared mailbox (named: Group Mailbox) created using Exchange Managment Console . I gave Full Access and Send As permissions to 10 users. They were able to read/send emails,  and to create some folders within this shared mailbox and also to rename these folders anytime they wanted.

Things went wrong when I added 'Full Access' and 'Send as' permissions to another user. Everyone except new user were unable to rename folders... I took over a laptop of new user and checked Outlook settings, but then discovered strange thing. Group Mailbox didn't appear in Additional Mailboxes for main account and even in account settings as a separate mail account !! Don't know how he added this shared mailbox to his profile. User said that this mailbox was there when he logged in to Outlook after I granted him 'Full Access'.

I deleted 'Group Mailbox' in his Outlook and added again through Additional Mailboxes option for main account. After this he could read and receive mails but couldn't rename folders !!!

Every user has unchecked "Download shared folders" option.
One of the users has 2 profiles A and B - in both profiles he added "Group Mailbox", but only in Profile B he can rename folders in "Group Mailbox". All settings are the same for every user...

Any ideas ? For some reason They really need to rename folders. I tried my best to sort it out...  Without success so far...