To make it easier to thread the wires through the fabric. I used a plastic bodkin. I zip-tied the connector to the bodkin, making it easy to feed through the fur. 

You want to place the first and last LED in the strand right in the center back, so it's easy to set up symmetrical animations. Use your thread ripper to make a hole in the seam at the center back of the hood or neckline of your coat.

Thread the light strand through the fur trim with the bodkin. I made another hole in the trim near the bottom of the coat - one that was big enough that I could get my whole hand inside to help coax the lights along. 

Pull the strand all the way around the coat, until the connector comes back out the same hole. 

Wiggle the lights until they're right at the outside edge of the trim. On my coat, the inside seam of the trim is sewn to the lining, but the inside trim seam doesn't connect to the outside trim seam, so the lights can pull away from the edge and into the center of the coat. If this is the case with your coat, add a few hand-sewn bar tacks here and there, connecting the outer and inner trim seams so the lights stay in place.

My coat has an inside pocket that's just perfect for holding the battery. If yours doesn't have this, I recommend getting a scrap of fabric and sewing one in there where you can reach it. I used my thread ripper to make a small hole in the fur lining and the bodkin to thread my USB cable up through this hole to plug into the Mini Sparkle Motion in the back of the hood. 

Once you're happy with the placement of the lights, trim the strand to length so the first light and last light meet in the back of the hood. Use heat shrink and hot glue or silicone tape to connect them together, enclosing the bare ends of the cut wire to waterproof the line.

This silicone tape is wonderful stuff. It's used for irrigation repair and fuses to itself in a waterproof seal. After a few hours it becomes one solid piece of silicone that needs to be cut off to be removed. It does a great job of holding everything in place and keeping dust and water out of your electronics.