Basically, Cut under the arms all around the coat. Or Cut the shape you want from the back of the coat. Or cut in to many squares and sew together Fur to Fur.
Hi Betty, that's a unique idea and one you could easily do using a carpet pad/mesh and sealing around the edges with carpet tape and a sturdy webbing around the edges or to piece together different sections of the garment. I hope you post what you've done for us to see.
Faux Fur Rug from a COAT! | Redo It Yourself Inspirations : Faux Fur