Please try this:

Open a new message

1. In the From choose Other Email Address

2. Click on the From button 

4. In the Address Book section choose Public Folders 
   
5. Type your Public Folder name and then enter 
   
6. Select your mailbox from the search results.
7. It should now look like this 
   
8. Send a test email.

Unfortunately, for the time being, you will need to do this for every email you wish to Send As from a public folder mailbox.  The shortcuts in the From toggle box just don’t seem to be functioning.