Yes, we begin to suspect before the end of the story that the lady was not the person Horace Danby took her to be. She was unusually calm on seeing Horace. This seemed strange. When she did not call the police, and instead asked Horace to take out all the jewels from the safe, even if it meant breaking it open, it seems suspicious. Moreover, it seemed highly unlikely that she would forget the number combination to open the safe. Therefore it was evident, before the story ended, that the lady was not the person Horace had taken her to be.