It is stunning. I can tell your grandmother was a woman with style.
The collar does still look like dyed Tuscan Lamb or some other high quality Lambskin or Sheepskin. I would really need to feel it to be certain. Tuscan Lamb's wool or fur feels really soft but has a very thick wooly feel when you put your fingers through it. Fox fur looks similar to it as well but it is a bit more fluffy and when you put your fingers through it, the guard hairs do not have that thick wooly texture that Lambskin wool has.
Shearling is shorn Lambskin or Sheepskin. Upon viewing the additional photo that shows more of your lining I can tell the lining is Sheared Muskrat or Sheared Nutria by the shape of the pelts, size of the pelts, the way they are crafted together, and the tiny little white furs where the dye color did not pick up which is commonly seen in both fur types after being sheared and dyed.