How to fix login screen (lightdm) orientation and prompt with my two monitors?

Support & Help Requests
,
#1

I have Ubuntu MATE 16.04.6 LTS installed on a system with two monitors.
They act normally when I login to default MATE 1.12.1 session.

But the LightDM login screen looks weird on both screens:

  1. 1600x900 normal landscape rotation

1600x900 landscape

  1. 1280x1024 left portrait rotation

1280x1024

Details about lightdm:

$ dpkg -l | grep -i lightdm
ii  liblightdm-gobject-1-0:amd64   1.18.3-0ubuntu1.1  amd64  LightDM GObject client library
ii  lightdm                        1.18.3-0ubuntu1.1  amd64  Display Manager
ii  lightdm-gtk-greeter            2.0.1-2ubuntu4     amd64  simple display manager (GTK+ greeter)
ii  lightdm-gtk-greeter-settings   1.2.1-0ubuntu1     all    settings editor for the LightDM GTK+ Greeter
ii  ubuntu-mate-lightdm-theme      16.04.7            all    LightDM theme and default configuration for Ubuntu MATE

$ cat .dmrc 
[Desktop]
Session=mate

I see this on every boot-up and currently I enter my password blindly.

How and where should I fix this problem?

Note: also asked on AskUbuntu without positive results (yet).