Cannot change login wallpaper in 10.15 Catalina?
Here's a simplified version of what you need to do (thanks to user3439894):


Put an image you want to use as login background somewhere in your file system (I used my Downloads folder in this example).
Reboot your Mac holding Cmd+R to boot into Recovery OS.
Open Terminal from the Utilities menu on the menu bar.
Backup/Rename Catalina.heic to e.g. Catalina.original.heic in  /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures/, e.g.:

cd  /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures
mv Catalina.heic Catalina.original.heic

Copy your desired image: cp /Volumes/Macintosh\ HD\ -\ Data/Users/[short_user_name]/Downloads/[image_from_step_1].jpg /Volumes/Macintosh\ HD/System/Library/Desktop\ Pictures/Catalina.heic


Note you can replace the destination path in the above command with just ./Catalina.heic as you should already be in the target directory if you performed the previous step to backup the original file.

Reboot into normal mode.
Change any option in System Preferences > Users &amp; Groups > Login Options to change the cached image.