The capability to sync the read/unread message state for IMAP is available in v4.1
This option is enabled by default for new configurations, but must be enabled for existing configurations (ie. if you're updating from v4.0 or earlier). To enable it:
Main Menu: Tools / PPTweaker / Misc page
'IMAP: Sync read/unread state with server'
After pressing OK, you will be prompted if you want to sync messages from POP Peeper to the server. The recommended action is YES.