Who is revealed to be the murderer in the play, The Mousetrap?

In the final act, Trotter pulls a gun out of his pocket, threatens to shoot Mollie, and reveals that he is Georgie, the older brother of a child who was murdered by his foster parents. Georgie and his sister were neglected and abused by the same people. It was Georgie/Trotter who murdered the woman in London and Mrs. Boyle. He is not realty a policeman, but only assumed that disguise to gain entry to the guest house.