Hi Natassia,
From your description, and what I know is commonly available out there, I would bet this is muskrat. Dyed with stripes to make it look more like mink, muskrat is a very versatile and relatively inexpensive fur that was popular (dyed like thta) in the 1930′s and ’40′s. If there is a tear that large, it really depends on the condition of the skin itself, not the fur, as to whether it can be sewn back up. Open the lining and see how stiff the skin feels. Use my directions from the article to sew it and possibly reinforce it with a leather patch from behind, after you finish sewing it. And wear it with extreme care, meaning, take it off before getting into a car, and just be very aware of the way you’re stressing it. No shoulder bags, nothing that will grab the fur in any way.
Good luck!