Chosen Solution

I recently had to replace my iPhone’s (5s) home button and touch ID with another iPhone (iCloud locked). I know the touch ID won’t function, when I turn on my iPhone a message appears (iPhone enable to activate touch ID), but what concerns me would this be a problem if I want to back up my iPhone to iTunes or restore the backup from iTunes, if yes would it be also a problem if I want to restore my iTunes backup in another iPhone 6 or another apple device ?

No. You’re good. There was an issue a little while back, called error 53, but the government made apple stop. It’s out dated now. You’re safe to backup and restore to any iOS device