No, since the Anniversary Update, a digital license can be tied to the account, and supposedly we should be able to use the activation troubleshooter to re-activate windows, but it doesn't always work as it should.I think you're confused. The Windows 10 license is tied your pc. i.e. your mobo, RAM, and CPU. So of course Microsoft recognized those parts when they were transferred to your sister's PC.
Your PC is no longer the same PC. Is has new core components and therefore it's a new PC (by Windows 10 installation standards).
Anyways, you can get a Windows 10 key on Ebay for like $4 if it's a problem.
https://support.microsoft.com/en-us/help/20530/windows-10-reactivating-after-hardware-changeIn Windows 10 (Version 1607 or later), link your Microsoft account to the Windows 10 digital license on your device. Then you can reactivate Windows using the Activation troubleshooter if you make a significant hardware change later.
Either way, in the end both me and my sister got both our systems activated, even if it wasn't as smoothly as it should.