The author of the article poses this question to law professors. Unfortunately, the professor made the answer to the question even more complicated than it needs to be.
The simple answer is this: if Gilbert Jr. is convicted of murder, then he cannot inherit from his father.
You cannot receive an inheritance from someone you intentionally killed. However, if the death is ruled accidental or if Gilbert Jr. is found not guilty, then he could very well inherit from his deceased father.
While these circumstances often make for interesting plot lines, in reality this is one area where the law is very clear.