Rotator cuff, impingement, shoulder pain, shoulder problems are an issue for many people but particularly for arm amputees. One has to be careful to not overdo it with either both shoulders (800m butterfly style swimming was what gave both of my shoulders the last kick) or with the dominant arm's shoulder (lifting weights, lifting groceries, lifting furniture, etc).
I got into some trouble in December 2008 so I got some physiotherapy. After my physiotherapist started me with some exercises, things got back to normal. Don't forget. One MUST exercise!
Both posture of the body and particularly the back, and the shoulders, should be trained. I use very light weights if any and if I have to increase the load, I increase the length of one series or the count of repetitions. I do not primarily increase the load by increasing the weight. My physiotherapist showed me a bunch of exercises to do, and from these, I find these are nice and helpful to do:
I find that doing these with the stump can be difficult when weights or pulling a string are involved. Either I leave the prosthetic arm on or I use a Theraband.
I find that shoulders cannot be trained well in isolation. Body posture should be trained along with it. Also here, building performance - not hypertrophic looking muscle - is the goal.
I do not do these to build hypertrophic muscle. These are done to build control and slow increase of power.