people after a stroke have different pattern of memory, and to some of them, this would be the best way to remember exercises. I assume this is with the goal in mind that the client exercises at home without you.
I would have absolutely no problem with a client taping a session with me. The only thing to consider is that no other people are in the video without their consent (particularly pertinent in a gym setting where they may get into the picture accidentally). However, I would prepare an introductory paragraph in which you state your own consent and the reason why this session is being taped. I would also state that this video must not be used to upload to a place like YouTube (unless you want it to be). I would also put that in writing and have the client and the person taking the video sign it.