I don't think the horse is sway back. I think that with about 100# or so and some muscle he will look like a different horse. You can see it in his neck and loins that he is underfed and under worked for a long time. He seems to have good legs and a nice shoulder. He has good depth considering his condition. BTW, A 15 year old horse should not be sway back.
I would start the first week just feeding and handling him but no riding. The second week would be lunging and ground work. By the third week I would have him under saddle but would wait until then or even the 4th week before riding. When I did ride him it would be very light work for a solid month, increasing it each week until I had him out for a couple of hours. I would not be jumping this horse for a while. He needs to come back slowly.
Many times a horse in that condition will be very lay back but as soon as you build them up they are a different horse altogether - just something to keep in mind.
You mentioned that a possible trade was involved. What is that about? How much do they want for the one you are looking at.