The client had a right to know, but Sherlock's decision certainly made sense considering that the client hadn't been particularly harmed, nor did he have any involvement in the final outcome.
If he had told her, it may have caused ill feelings between the girl and her mother since the mother was involved in the deception. So I'm on the fence; the girl should know the truth, but why hurt the mother/daughter relationship.
For example, what do you think of Holmes's decision not to share his findings to his client?