Is there any way to remove wrinkles from a fake leather coat?

Have you tried calling a dry cleaner and asking them?

Do NOT IRON IT! It will melt. Also, there should be a label on the inside with washing instructions. You mention nothing of a lining or anything, so I really can’t help you with washing instructions. There should be a label on the inside. If it doesn’t have wording on it about washing it should have international symbols like this:

http://www.wayway-group.com/upload/knowledge/30b3274c6649337c359432b9b3eeb01f.jpg

Generally, wrinkles will fall out of polyurethane if they aren’t too bad. Just leave it hung up for a while on a really good hanger (not a flimsy wire hanger, but a nice broad one made for jackets) Wearing it can also help, as body heat may help the fabric straighten.

If you feel the wrinkles haven’t fallen out after a few wearings, you could try a blow dryer on lowest heat, held away from the fabric. The polyurethane should be just warm as you smooth your hand over the wrinkles. This may take a bit of time, but time is better than melting your new coat.