It's not authentic. As others have mentioned, its an Adidas Swingman jersey. The numbers and names are sewn on but its not an authentic game jersey. There's a difference.
$39.99 is a great price for a Swingman jersey, though. I'm pretty sure those things retail in the $60s or $70s now (possibly more).
An authentic will run you anywhere from the high $100s to the $200s depending on the retailer.