Yep, here in sunny Florida, a permanent resident can own a gun too. I have several British friends who have gotten into the shooting sports.
One friend here at work married an American girl, got his citizenship a few years back. He was very happy to be able to vote (a good conservative Republican, too!), became an NRA life-member and took the hunter safety course with his two older sons.
Another was in the British Army, and is great to talk to about the weapons and equipment used by the Brits recently.