Suppose I copy the Program Files and Windows folder (especially the Windows\system32\config folder), format the HDD, and reinstall Windows.
Now, as soon as Windows finishes copying the files, instead of booting into Windows to continue the installation, you would boot into an other OS, and copy back the files you previously copied. Then, you would boot into Windows and it should be pretty much the same before formatting.
Would that work?
It should work, I can't see why it wouldn't work
Btw, this would be done one the same computer, not two different computers.
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