Firewall configuration:

FrontEnd --> Master 	3905
Master --> FrontEnd 	666
FrontEnd --> Backend 	666
Backend --> ldap 	3905

666 is the lmtp port
3905 is the mupdate port

I don't use PAM.
The user murder is useradded in Master server.
And proxy_murder is useradded in Background server.

###################
Frontend: 10.1.1.73
###################
imap.d

configdirectory: /var/lib/imap
partition-default: /tmp
admins: cyrus
sievedir: /var/lib/imap/sieve
sendmail: /usr/sbin/sendmail
hashimapspool: true
sasl_pwcheck_method: saslauthd
sasl_mech_list: PLAIN
tls_cert_file: /usr/share/ssl/certs/cyrus-imapd.pem
tls_key_file: /usr/share/ssl/certs/cyrus-imapd.pem
tls_ca_file: /usr/share/ssl/certs/ca-bundle.crt
mupdate_server: 10.1.1.71
mupdate_username: murder
mupdate_authname: murder
mupdate_password: murder
server_background_password: proxy_murder

#here I specify murder password
proxy_authname: murder

cyrus.conf

START {
  recover       cmd="ctl_cyrusdb -r"
}
SERVICES {
  imap          cmd="imapd" listen="imap" prefork=5
  pop3          cmd="pop3d" listen="pop3" prefork=3
  lmtpunix      cmd="lmtpproxyd" listen="/var/lib/imap/socket/lmtp" prefork=0
}

EVENTS {
  checkpoint    cmd="ctl_cyrusdb -c" period=30
  delprune      cmd="cyr_expire -E 3" at=0400
  tlsprune      cmd="tls_prune" at=0400
}

###################
Backend: 10.1.1.93
###################

imapd.conf

autocreatequota: 20480
hashimapspool: 1
tls_ca_filetequota: 204800
sasl_mech_list: PLAIN
configdirectory: /var/lib/imap
admins: cyrus
#sievedir: /var/lib/imap/sieve
sasl_pwcheck_method: saslauthd
tls_ca_file: /usr/share/ssl/certs/ca-bundle.crt
autocreatequota_units: 1048576
tls_key_file: /usr/share/ssl/certs/cyrus-imapd.pem
sendmail: /usr/sbin/sendmail
autocreateinboxfolders: 1
partition-default: /var/spool/imap
quotawarn: 70
autosubscribeinboxfolders: Posta inviata|Posta eliminata|Bozze|Posta in arrivo
servername: mail01.postafvg.it
mupdate_server: 10.1.1.71
mupdate_username: murder
mupdate_authname: murder
mupdate_password: murder
proxyservers: 10.1.1.73


cyrus.conf

START {
  recover       cmd="ctl_cyrusdb -r"
}

SERVICES {
  imap          cmd="imapd" listen="imap" prefork=5
  pop3          cmd="pop3d" listen="pop3" prefork=3
  lmtpunix                cmd="lmtpd" listen="/var/lib/imap/socket/lmtp" prefork=1

}

EVENTS {
  checkpoint    cmd="ctl_cyrusdb -c" period=30

}

###################
Master: 10.1.1.71
###################

cat imapd.conf
configdirectory: /var/lib/imap
partition-default: /tmp
admins: cyrus root murder
mupdate_server: 10.1.1.71
mupdate_username: murder
mupdate_authname: murder
mupdate_password: murder

cyrus.conf

START {
  recover       cmd="ctl_cyrusdb -r"
}
SERVICES {
mupdate cmd=mupdate -m" listen="mupdate" prefork=1
}
EVENTS {
  checkpoint    cmd="ctl_cyrusdb -c" period=30
  delprune      cmd="cyr_expire -E 3" at=0400
  tlsprune      cmd="tls_prune" at=0400
}