Fake leather boasts all of the aesthetics of real leather at a fraction of a cost. While real leather has a very distinct smell to it, fake leather sometimes has a smell of its own. This smell can either come from the chemicals used to make it or from the packing materials used to ship it, but either way it's more than likely a smell you want to get rid of. There are several proven methods that can help to eliminate the smell.
Wrap the jacket in newspaper and set it in a cool dark dry place for 24 to 48 hours. Newspaper is great for absorbing odours.
Put vodka in a spray bottle and lightly mist the jacket before setting it outside to air out. Hang the jacket somewhere in the shade to get some air; sitting in direct sunlight for too long may discolour it.
Place the jacket in a box or bag with a piece or two of charcoal. Seal the bag or box up and let the jacket sit for 24 hours.
Lay the jacket on a flat surface such as a table and sprinkle baking soda all over it. Let the baking soda sit on the jacket for 2-4 hours before flipping it over and repeating the process.
Place the jacket in a bag with 7 cotton balls dipped in vanilla extract. Make sure that none of the cotton balls are touching the jacket and seal the bag up. Leave the jacket in the bag overnight and check it in the morning. Repeat the process with fresh cotton balls if necessary.
Sometimes the chemicals that are used to make the jacket emit a smell that you may not be able to get rid of. If nothing works, you may have to send the jacket back to the manufacturer.