Hi, Tas!

I think you try to use IMAP Offline account?

As I know, there is no possibility to get any folders and emails outside inbox.

You can try IMAP Online, then you will be able to receive all emails. But only online.

As I seen you can replicate IMAP Online database to local storage, but I was not able to do it.

<<HELP FROM IMAP ONLINE>>
Creating an IMAP replica 
As described earlier, an Mail (IMAP) database doesn't store messages locally. Depending on your needs however, you may want to create a replica of your Mail (IMAP) that does store messages locally. For example, you may need to disconnect from the network to go on a business trip, but you need to read mail. 
When you create a replica, you pull messages from all your IMAP folders to a separate local database. 
To make a replica of an existing Mail (IMAP) database: 
Open the Mail (IMAP) database. 
Choose File - Replication - New Replica. 
Change the File Name. For example, if the Mail (IMAP) database is named IMAP.NSF, change the file name to IMAPREP.NSF. 
Click OK. 
Open the Replicator page. Notice there is a new replication entry for your Mail (IMAP) database. 
Click Start to begin replication. 

When replication is finished, double-click the icon on the IMAP replication entry to open the IMAP replica. You can now read and send mail messages locally. If you are disconnected from your network, sent mail is held in the "Outgoing mail" database (SMTP.BOX). When you reconnect and restart replication, your mail is sent. 

Please let me know if you can do it.

Max