As far as I can tell her having the gun isn't the issue. she legally owns it and it's a legal gun to own in NJ therefore she can have it in NJ.

The issue is she left it unattended in the glove box of her car

https://nj.gov/njsp/firearms/firearms-faqs.shtml

​

How do you transport firearms?

Firearms shall be carried unloaded and contained in a closed and fastened case, gunbox, securely tied package, or locked in the trunk of the automobile in which it is being transported.  If the vehicle does not have a compartment separate from the passenger compartment, the firearm and or ammunition shall be in a locked container other than the vehicle's glove compartment or center console and kept farthest from the driver.