To manually rearrange icons you must have Auto-arrange turned off (Right click desktop, choose Arrange Icons by. . ., then check/uncheck Auto Arrange). Otherwise the icons will either pop back where they were, or put themselves back on a reboot.
HTH,
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Many discussions run on to the point at which they become impossible to follow, I find.
So here is a solution to one of those discussions but, so-to-speak, highlighted
If you want to re-arrange your desktop icons, then simply hold down "left click" on the icon and move it wherever you want it to be.
If you want to delete an icon, then simply "right click" and you will be given options, e.g. you will be advised that either "this will only remove the short-cut", or that you are about to remove a program.
What could be simpler?

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