I have an Android 5.x smartphone ("phone 1"), which was using my Google account. Recently, I've started using different one, so I've (pretty confident that I've) dropped Google account on "phone 1", and then after having all things set up on "phone 2", I've made a factory reset on "phone 1"
However, when my son is now trying to begin using "phone 1", the initialization procedure REQUIRES him to use the account that was used on this phone before !! I presume this is good for protection against thieves, but how can I allow him use this phone ? I don't want to login under my account on that phone again
factory-reset
tag to your question. What you're encountering here is called "Factory Reset Protection" (FRP). Please check our factory-reset tag-wiki for the corresponding section.