[Dovecot] Public mailboxes

[libero1]

Ciao everbody,
I have a simple question for who has a few experience with dovecot.
I want to share a mailbox with some users, I configure dovecot and now in my thinderbird I can see the public namespace. The problem is that I cann't see the "inbox" of the mailbox, in other words when a mail arrive in this mailbox I can not see it, but only what is in other folders. 
Why? Is it normal? What can I do to let my users to see new messages?


Thanks for you help.
Bye