Bücher unter dem Mond

I loved this book, but there is a mistake in the end :c I'd like to know if someone agrees with me ^__^

SPOILER!!!!!!!!!!!!!

Yes, I did. In the book Hercule Poirot's Chhristmas he says the murderer was the superintendent Sugden, Poirot says he also stole the diamodons of Mr.Lee, but how Sugden knew he has diamonds in his room if nobody but Pilar (who wasn't even the true Pilar and it's was her first time in England and never saw Sugden before to tell him about them)? Here is the paragraph that isn't clarified by Agatha:

Yes, I did. In the book Hercule Poirot's Chhristmas he says the murderer was the superintendent Sugden, Poirot says he also stole the diamodons of Mr.Lee, but how Sugden knew he has diamonds in his room if nobody but Pilar (who wasn't even the true Pilar and it's was her first time in England and never saw Sugden before to tell him about them)? Here is the paragraph that isn't clarified by Agatha:

‘No, you killed him before you left the house the first time. No one saw him alive after you left. It was all so easy for you. Simeon Lee expected you, yes, but he never sent for you. It was you who rang him up and spoke vaguely about an attempt at robbery. You said you would call upon him just before eight that night and would pretend to be collecting for a police charity. Simeon Lee had no suspicions. He did not know you were his son. You came and told him a tale of substituted diamonds. He opened the safe to show you that the real diamonds were safe in his possession. You apologized, came back to the hearth with him and, catching him unawares, you cut his throat, holding your hand over his mouth so that he shouldn’t cry out. Child’s play to a man of your powerful physique.’


Think by yourselves and let's discuss! ^^