First, Local Folders are local to the PC, and are not available on phone. You can view and respond to messages from phone, but your sent messages will remain on phone if using POP there, and not visible on PC. Likewise, you will not see messages on phone that were sent from desktop. Also, both phone and desktop will be able to view incoming messages only when the other device has not deleted them. Consider, you're reading from the same source, so if you delete from phone when downloading, it won't be visible on desktop. If you want both to be in sync, the only solution is to use IMAP for both.

Thanks for the reply. After reading your reply I searched the TB settings and found the option "Leave Messages on Server Until I Delete Them". At present this is unchecked and so the emails are auto deleted from the server. I would guess there is something similar on the Mobile App settings as well. Thanks again.