There is a good Microsoft article, explaining how to fix synchronization issues between Exchange and Outlook, when some Exchange objects do not appear in Outlook. However, a small part should be added to the article.
When a user cannot see the content of a particular public folder, even if he/she is an owner of it and none of the steps from the article above helps, try this
1. Make only one user an owner of a public folder with synchronization issues
2. Turn all other Owners into Publishing Editors
3. Run the user’s Outlook as follows
4. Be aware that the user will lose all the views created in Outlook