Yes, one does 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 enough. 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 seemed suspicious. Moreover, it also seemed unlikely that she would forget the numbers 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.