Thanks Been Burned!It's authentic.
15238 is a convertible Zoe but it appears your bag is missing the removable longer strap.
I found this picture of the bag showing the crossbody strap:
cafashionstore.com/images/Coach%2015238%20.jpg
15240 is a similar style but a tote:
natalieshop.com/wp-content/uploads/2010/11/Coach-F15240-B.jpg
I do not have the extra strap

you peeps are the best

Thanks RC