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Can I replace my 5s home button which has no Touch ID with a 6s home button with Touch ID and get my Touch ID back
6s home button is not even the same thing, physically it won’t fit, electrically probably wired differently, plugging it in may fry your phone. Cryptographically, every iPhone Touch ID button is unique and not replaceable. Unless you have access to Apple tools, you don’t repair Touch ID period.
No you can not as the touch id is recognised with the original home button not with the phone itself. The only way now to get back the touch id would be a call/visit to apple to get it replaced.