It's pretty hard to confirm dimensions by viewing your pictures, but I would take the threaded black piece from your fridge to your local big box store, along with the dimensions of your copper tubing, which should be 1/4". From this point, you can either pick up an adapter in brass to join the two together or you could always cut the female threaded fitting on your existing incoming water source and use a compression fitting with a ferrel on your house side, with a threaded male fitting on the fridge side. You can also show these pictures to a plumbing house and they probably have an adapter which will allow for a real quick installation.