I just took a quick look at the FL. CCW application, and I did not see anywhere on it, "have you ever been denied the right to carry a firearm".
Also I don't see how a NJ ccw denial would affect your being able to get a ccw in a shall issue(American state). You aren't getting denied because you have any criminal charges, or anything that a free state would reject you for. It's because the most liberal anti-gun state in the country, said you had no justifiable need. If this came up on your new states ccw application, a simple explanation should be sufficent.