Is it permitted to install the backup image of Windows 10 to a New bigger hard disk in the same PC. After that I will use the new hard disk only and format the old one.
Yes, that is allowed.
It should not even change anything with the activation status, meaning, Windows should continue being activated. Should Windows at some point in the future try activating again (because you did more hardware changes or whatever), also this should work without problems.
Although changing the motherboard out may require a phone call to MS to activate, which may or may not succeed, depending on which side of the bed the rep got up on that morning and how kind and tolerant you are with them.
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