Если хотите, можно упростить конфигурацию Exim использовав
аутентификацию Dovecot

vi /etc/exim4/exim4.conf

...
#AUTHENTICATION CONFIGURATION
begin authenticators
auth_plain:
    driver = dovecot
    public_name = PLAIN
    server_socket = /var/run/dovecot/auth-client
    server_set_id = $auth1

auth_login:
    driver = dovecot
    public_name = LOGIN
    server_socket = /var/run/dovecot/auth-client
    server_set_id = $auth1

auth_cram_md5:
    driver = dovecot
    public_name = CRAM-MD5
    server_socket = /var/run/dovecot/auth-client
    server_set_id = $auth1