this is log of mail server, here it seems all right
Jul 3 11:54:27 vps2p courier-imapd: Connection, ip=[::ffff:127.0.0.1]
Jul 3 11:54:27 vps2p courier-authdaemon: received auth request, service=imap, authtype=login
Jul 3 11:54:27 vps2p courier-authdaemon: authpsa: trying this module
Jul 3 11:54:27 vps2p courier-authdaemon: authpsa: authentication request with service='imap' authtype='login' authdata='user@domainname.it.passwordxxx.'
Jul 3 11:54:27 vps2p courier-authdaemon: authpsa: auth_psa_common(user='user@domainname.it', pass='passwordxxx')
Jul 3 11:54:27 vps2p courier-authdaemon: authpsa: password for 'user@domainname.it' is plain 'passwordxxx'
Jul 3 11:54:27 vps2p courier-authdaemon: authpsa: sysusername=popuser, sysuserid=110, sysgroupid=31, homedir=/var/qmail/mailnames/domainname.it/user, address=user@domainname.it, fullname=<null>, maildir=<null>, quota=<null>, options=<null>
Jul 3 11:54:27 vps2p courier-authdaemon: authpsa: clearpasswd=passwordxxx, passwd=<null>
Jul 3 11:54:27 vps2p courier-authdaemon: authpsa: about to check auth.clearpasswd: pass='passwordxxx' auth.clearpasswd='passwordxxx'
Jul 3 11:54:27 vps2p courier-authdaemon: Authenticated: sysusername=popuser, sysuserid=110, sysgroupid=31, homedir=/var/qmail/mailnames/domainname.it/user, address=user@domainname.it, fullname=<null>, maildir=<null>, quota=<null>, options=<null>
Jul 3 11:54:27 vps2p courier-authdaemon: Authenticated: clearpasswd=passwordxxx, passwd=<null>
Jul 3 11:54:27 vps2p courier-authdaemon: authpsa: auth_psa_common() callback returned 0
Jul 3 11:54:27 vps2p courier-imapd: LOGIN, user=user@domainname.it, ip=[::ffff:127.0.0.1], port=[43027], protocol=IMAP
Jul 3 11:54:27 vps2p courier-imapd: LOGOUT, user=user@domainname.it, ip=[::ffff:127.0.0.1], headers=0, body=0, rcvd=24, sent=286, time=0, starttls=1