The cross-body stretch you are using is commonly used to help stretch the posterior capsule of the shoulder. The posterior capsule is a band of fibrous tissue that interconnects with tendons of the rotator cuff of the shoulder. The rotator cuff is made up of four muscles and their tendons. They cover the outside of the shoulder and form part of the posterior capsule to hold, protect, and move the joint.
If the posterior capsule is too tight, internal rotation motion of the shoulder can be limited. That type of shoulder tightness can lead to shoulder problems such as impingement, rotator cuff tears, and damage to the labrum. The labrum is an extra rim of fibrous cartilage around the otherwise shallow shoulder socket. It helps keep the shoulder in the joint and prevent dislocations.
Check to see if your shoulder internal rotation is limited by reaching behind you with one arm and touch your spine. Reach up as high as you can. Do the same thing with the other side — can you reach to about the same point with either hand? Can you reach back there at all? If you have trouble with this motion, you may have a tight posterior capsule.
What you are doing with the cross-body stretch is what would be recommended for anyone with tightness of this type. Since you may have some limitations, go slowly and don’t overstretch. Hold the stretch for a slow but steady count of 30. Keep breathing while stretching. You should see a difference after applying this stretching technique three to four times each week for a month but you’ll probably have to keep it up on a regular basis to maintain the increased motion.