All of the responses are right on the mark, especially Carol’s and Chris’s. It’s a collaborative, team process. In the end it’s not who is necessarily the most qualified, it’s what’s best for the client. Physical therapists are extensively educated in the treatment and training for rehabilitation from injury. A personal trainer, without PT education, does not have that background.
But that’s not the issue. The issue is for the personal trainer to continue on with the PT’s recommendations to provide the highest quality continued training regimen. It requires a clear and comprehensive communication, not a competition.