The Puzzle Mystery of George Lorimer

There are two big issues or even plot holes that we have to deal with in this short story. If George Lorimer was going to inherit from the impoverished garbage artist, Uncle Henry, then why wouldn't he have inherited from rich uncle Anthony for the same reason? I think Christie could have avoided this issue by having Amelia Hill tell Poirot that Anthony's will specified all his money would go to a specific charity but she didn't do that. More significant though is our second plot hole, which is that Lorimer created this problem for himself by murdering Uncle Henry the same day Uncle Anthony died. There is nothing about this impersonation scheme and alibi that had to have been done the very