You know, I really believe that small piece is a proliferation that broke off during transit. I recognize that hybridizer just from the stapled label, and yes he does have a great reputation. I received my second order for the year from him yesterday, and I had a prolif attached to the remains of a dead scape -- and I'm thrilled to get it because it's one of his new summer introductions. So I am getting two plants of it!
I think you should put that small piece in a small glass or plastic cup with water covering the roots, and change the water every day. Then when the roots grow a bit I plant them in pots. And this one is already showing some root growth just from overnight soaking.
Here is my plant and prolif from yesterday -- and look -- the leaves are already growing! I always soak the roots overnight before planting, which is why the roots on the mother plant are wet.