With any type of washer, the least agitation possible is the best choice. Fill the washer to a medium level with cold water. Add a tiny amount of mild, color safe detergent like a wool wash (Woolite). Place the fake fur garment in the washer. Allow the faux fur to soak in the water and detergent solution for 15 minutes. Do not soak longer or you may damage the faux fur's backing fabric.
After 15 minutes, set the washer to drain and spin. Switch to the rinse cycle and allow the washer to fill with cool water. Do not allow the machine to agitate. Drain and spin again. If you feel the garment needs an additional rinse, do so at this time. Again, no agitation!