Change the Zorin menu icon for custom icon

I want to change the Zorin icon in the menu for a custom icon, I have tried to do it by replacing the files containing images of the Zorin logo in the directory usr/share/icons/Zorin/... in several folders like /scalables/places or /16x16 or /32x32 but none of these changes to successful result. Note that the custom icon has the correct format to work in the menu (32x32px and PNG format). Any suggestion to make this change?

I did similar by merely removing the dock and using Cairo-dock.
Now, I have reverted the app menu icon back to a modified Zorin icon... On the Cairo Dock still.

I have wondered the same question. So, I am going to see if I can figure out a way. Will update.

EDIT: I should point out, on Zorin 12.4 Core, My custom Icon called start-here.png replaced the default icon when I applied my custom icon theme.

I've been tinkering and not got far - because I had forgotten that gksu does not work any more - it is something else - brain overload!

https://itsfoss.com/gksu-replacement-ubuntu/

Love "Syntaxxx Err0r" post on this topic!