I just transplanted some of my wild black raspberries a couple of weeks ago and they are all doing fine. Just make sure you get some good roots on it and give it plenty of water every day.
I know how you feel, I found one trying to grow along side our sidewalk a couple of weeks ago. Then in my flower bed in the front side of the garage I found about 6 Tomato plants. They are all looking nice in my garden now! lol
I also have a raspberry bush that popped up in my rock garden last...