It would be great if anyone reading this thread could solve this mystery. Even the descendant is unsure of the exact status of claimants.
I have never come across, in my perusal of thousands of pension file documents (many of which are online), of any person, who was either accused of, or confessed to fraud, being continued in the payment of the United States government pension. If fraud was detected, payment was immediately ceased. Yet, the person in Wisconsin, who claimed the pension, continued receiving it up to his death.
Furthermore, if fraud, with the complicity of the person in New Zealand, was detected, no doubt the New Zealander would have been disbarred his profession, or some action taken against him.
As I stated before, if anyone is able to solve this enigma, please do so.