
If the last owners had no time for a young pup, my money would be on boredom as the trigger, and it's likely becoming a habit.
Best thing you can do is ignore it or distract her so she forgets what she was doing outside, and clean up constantly so she doesn't get the opportunity.
I sympathise though, I know how unpleasant and frustrating it can be; I've had one who did it initially from boredom I believe - full time owner and a smart dog (she was a dobe, and a very high energy one) - with her it became habit. I have two who do it now for other reasons.
The one thing you mustn't do is tell her off for doing it - you'll just turn it into forbidden fruit so she'll get more sneaky, or you'll make her think it's something valuable so she'll try harder/eat faster. Ignore, distract, clear up! If you have a dog flap - shut it for a while until the habit is broken.
As for shedding - my lab girl is a sod for it, sheds like nothing else all the time, has all the while I've had her (2 years in May, she's 7).