Want desktop icons to stay put after reboot.

Plenty of desktop icons & shortcuts lay on the desktop.

Want to assign them into groups rather than A-Z.

But on reboot the disobedient gremlins scurry back to their old columns. Neat & tidy, but I want them to remain where I assigned them. Here is the setting I'm using -

Strange, they should be staying right where you put them.

This issue may happen if there are some themes which are installed on the computer, that interferes with the working of Desktop icons.

Perform the steps mentioned below and see if it helps.
a: Right Click on an empty space on the desktop, and then click Personalize.
b: Then Click Change Desktop Icons option present at the Top left corner.
c: Uncheck the option Allow Themes to change desktop icons.
d: Click Apply and then Ok.

Source: Desktop Icons change the order after restart - Microsoft Community