This question already has an answer here:
I don't understand how does the Elder Wand ownership work. Draco disarmed Dumbledore and gained ownership of the Elder Wand, but when exactly does this switch happen. What if Dumbledore picked up the wand after being disarmed? Was Dumbledore it's owner up until his death, and only then did Draco attain ownership because Dumbledore never touched the wand after being disarmed until his death and that counted as Draco defeating him, or did the ownership switch to Draco right after disarming Dumbledore? If so, what if Dumbledore picked up the wand then, would it disobey him?
It seems a bit weird to me that ownership would switch to an attacker right after disarming it's owner because disarming doesn't really count as defeating an opponent.
EDIT after some discussion in comments:
"I'm putting the Elder Wand," [Harry] told Dumbledore, who was watching him with enormous affection and admiration, "back where it came from. It can stay there. If I die a natural death like Ignotus, its power will be broken, won't it? The previous master will never have been defeated. That'll be the end of it."
Harry Potter and the Deathly Hallows Chapter 36: "The Flaw in the Plan"
Bold part of the quote doesn't hold true if disarming an opponent gains you ownership of the Elder Wand. Harry says that if he dies a natural death its power will be broken, but that is not really true if he can get disarmed, get the wand back and still win the duel he is in (or the unlikely scenario of him running away after getting disarmed) and still die a natural death but the wand's power will not be broken as after that disarming he is no longer it's owner.
UPDATE: I would disagree with the question being a duplicate. I understand that Draco unintentionally and unknowingly became it's owner, but my question is when exactly does this switch of ownership happen which the linked question does not answer.
UPDATE 2: The question you marked duplicate is actually not a duplicate as there is no answer about which exact act gives a person ownership of the Elder Wand.