Generally speaking, the time that any injury takes to heal depends upon the type of injury, the severity of the injury, and the health of the individual, including mental health and attitude. I'm pretty sure that some types of tears heal more slowly than a simple fracture, for example. I've had a couple of torn ligaments in my life, and they were much more painful and problematic than the various broken bones I've also had, all of which healed quickly. (Am I a klutz or what?)
I expect that it's up to the individual's medical practitioners to determine how much time any particular injury can be expected to heal to the point where the person can engage in physical rehabilitation, and that's important, because without PT, many injury sites involving major muscles can't fully recover to the point before the injury, due to lack of use.
So, Ellie, you need to know what your father's doctor says about this injury, and what recommendations have been made for physical therapy. If the injury is past the point where the doctor says that PT should have begun, that's the next step. If your father refuses to do PT because of pain, that's a problem, mentally and emotionally, because he needs physical therapy to re-learn how to use his shoulder without fear.
If he's done the PT and is not experiencing any positive changes, then TMS is a likely culprit, but if he's resistant to that, your chances of convincing him are probably not great. This may not be a battle you can win, but don't beat yourself up about it if you fail - because at least you tried! And you can try again in the future if he keeps complaining and not doing anything.
Good luck,
Jan