This is what the finished pocket will look like, so you can get a sense of where this post is going. We will be installing the pocket bag (the red fabric visible in the photo) into the slit opening we made earlier.

Begin by bringing the seam allowances to the front of the section.

Pin both seam allowances to one side (here I’ve chosen the left side but either side will do).
Comb the hair off to the right, and pin. This keeps it from being sewn into the seam.
Lay the right pocket bag, right sides together, on top of the fur. The opening of the pocket bag will fall right on top of the opening in the fur.
Mark a stitching line on the back side of the fur–this seam will sew the right side of the opening to the pocket bag.

Stitch along this stitching line, sewing through both fur and pocket.
Trim the excess seam allowance.
Turn the right pocket bag through the opening…
….and pin to the back of the fur to keep it out of the way.
Now, pull the other seam allowance off to the right…
….and comb and pin the hair out of the way.
Pin the left pocket bag over the opening.
From the back, sew right next to the folded edge of the first pocket piece, to sew the fur to the opposite pocket bag. Stitch between the pins here.
Here is the left pocket bag sewn to the fur. Trim the seam allowance here as well.

Turn the other pocket side through the opening. Since this garment section has the center front to the right in this photo, fold the right pocket piece towards the center, and pin near the edge. Since you can’t press these pockets, you’ll…