Does anyone have good corrective exercises for someone with lower back pain due to hip joint problems?

I have a family member who had one hip where the ball and socket joint has been fused together since birth. This has 2 major effects on his body: #1 - it limits certain hip motions, especially any kind of rotation on that side. For example, he can't sit "indian style" or do a butterfly stretch simply because his hip won't rotate that way. #2 - it makes one leg slightly shorter than the other. He does have a shoe insert that helps with this, but I don't believe the insert is necessarily correcting the problem.

He is 53 years old and was very active in his younger days. Now, he's a little less active, but he did run a half marathon last year and is still at a fairly healthy weight (maybe 10-15 pounds over optimal weight). The problem is, as he gets older, a number of things are "catching up with him." He has a lot of back pain when he wakes up in the morning and I believe some of it has to do with years and years of this hip/leg issue affecting his posture and lower back muscles.

Is there a good corrective exercise that can perhaps relieve some of the pressure on his lower back that is being caused by the differing leg lengths? I'm also looking for good exercises that can support his back and hips without doing more damage.

Any help or ideas are appreciated!