LaRue and Susan make good points. One thing I would add is that you may want to find out how long the client has been training with the other trainer and what their relationship has been. I assume that you have an opportunity to talk with the other trainer. Do not hesitate to call him when you have questions.
I remember a situation when a client of mine moved to another city and hired a trainer there. By her account of the story, it was war within weeks, and I could never understand why he never picked up the phone to call me and ask. I believe that his greatest shortcoming was that he was not me, and I am sure I could have made this a successful client/trainer relationship.
We all have our own approach to training, and it is important that you do not inadvertently contradict what the client was told before. I like LaRue’s suggestion of gradually changing towards your training.
I wish you good luck.