What are some things I can do to help my dog’s weak leg.

I just adopted a dog from the shelter this week. He was hit by a car about a year ago but they told me he had fully recovered from it. However it’s very clear that his back left leg is much weaker than the rest. when we asked the vet they said it’s likely because his past owner didn’t get him the rehab he needed. he has a hard time jumping onto the couch and needs to be lifted in and out of the car. he also drags that leg while walks. The snow is clearly bothering his leg and if we’re out for more than 5 minuets he starts hopping on the other three legs. We got him some boots to try and keep his paws warmer and help with the dragging but he hates them. if we even manage to get them on he runs off and immediately pulls them off. is there anything i can do to help strengthen the leg at least a little? the vet said because it happens so long ago therapy would likely be a waste but i’m afraid it’s hurting him and want to do anything i can to help him.