Does the trainer have to be part of the implementation project team?
They dont have to be. But if they havent been then they do need to be brought up to speed as to how the software modules were configured and other relevant items that only the project team would know. The training could have bad outcomes if the trainer and the project team are not in sync. This doesnt have to be a big deal, but a coordination meeting does should be held to discuss the status of the implementation, the training dates, the training agenda, special needs and nuances of the people being trained, and things you DONT want to be trained on.