How to change the lightdm background image in the greeter window'

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Login manager and users GUI are gone

Good question. Here are some links with explanations about this problem and also some workarounds: Here is a perfect working solution by reverting to slick-greeter: Extra background info and some workarounds for if you want to keep using 'Arctica' greeter, in the following thread are several ways to bypass some of the problems:

EDIT: See also this thread

How to change login screen background?

Some things changed under the hood which resulted in a bug. See this: and this: and the "won't fix" answer of the author. so you have to edit a configfile manually: sudo pluma /usr/share/glib-2.0/schemas/30_ubuntu-mate.gschema.override and change the background= entry then recompile the schemas: sudo glib-compile-schemas /usr/share/glib-2.0/schemas/. This seems to be the accepted workaround for the time being. It lacks a bit in elegance I'm afraid. But it works pretty well.