You must "first possess" a FID card to transport a long gun unless you're transporting within one of the exemptions. The exemptions are when traveling between: home, range, gun shop. Transporting to hunt with a hunting license is also an exemption.
If your spouse has a hunting license and is transporting to hunt, it's legal. If she's transporting to shoot trap at a range, it's legal. If she's transporting to shoot trap at her dad's farm, it's a felony if she doesnt' have an FID card.
Stupid, stupid NJ laws.