A wording change has to be made first: "If A claims that his money bought the item..." is false. His money did not buy the item. At the time of purchase, it was not owned by him. It was owned by the organization. Also, money does not buy things. The organization buys things. Money is used to pay for things.
The wording needs to have a past tense, and a rewording: "If A claims that the money he owned in the past was used to pay for the item..."
Now we can address the fungible claim. Neither A nor B can make this claim. If one were to follow the serial numbers of the dollars actually used to make the purchase there is a very strong likelihood that the bank actually gave the organization some different physical dollars. Neither A's dollar nor B's physical dollar was actually used in the purchase.
This then forces both A and B to admit that the physical dollar is not the thing that matters, it is the essence of the dollar that has the buying power. And, in this case, it is illogical for A or B to make the first claim that their physical dollar had anything to do with the purchase at all! An IOU might have sufficed.
The only valid way for A and B to divide credit for the actions of the organization is for the civilization around them to divide it for them. Consider, the reason A and B are making these claims in the purpose is that they wish the purchase to be attributable to them. Attribution is an act by people. If the civilization agrees to attribute the purchase to A or B, they are welcome to do so. Likewise the civilization may choose an arbitrary phrase like "A bought half of the item," even though the item does not divide cleanly in two.
This is called divorce.