A small tear in an expensive fur coat can be alarming. It can also be quite costly to pay for someone else to do it. Fortunately, it's not difficult to repair, if you have some basic sewing skills and a little patience. No matter what type of fur it is, the technique will be basically the same.
Locate the tear, and find the closest point where the lining is attached to the fur, assuming the coat is lined.
Carefully undo the seam with the seam ripper to make an opening wide enough to access the underside of the tear on the fur.
Cut a length of the artificial sinew long enough to sew the tear. Split the sinew by unravelling it into a much thinner segment. You don't want it to be too bulky. Thread it into the leather needle, and tie a knot at the end.
Stitch the tear from the inside of the fur using a wrap stitch. Be careful not to gather too much material into your stitch, as you want it to be as clean as possible. Remember that the underside of fur is leather, and you may need to pull the needle through the leather with the needle-nose pliers. Use the thimble on your opposing fingers, because leather needles are very sharp and will cause you to bleed when you poke yourself. Check the outside to see how it looks, and tie it off at the end.
Gently stitch the lining back together with a matching colour thread with your standard needle.
Leather needles are also called "glover's" needles. You can buy glover's needles and artificial sinew at most large craft stores.