1500W? At 12V that's 125A - That is fucking dangerous! Most sockets are rated at 20A. Most inverters that are >300W use crocodile clips, or preferably screw-down terminal rings. The cable looks way too thin too. That's a fire waiting to happen....
In my experience, most car sockets struggle to deliver 10 A and might be fused at 20 A (but a fuse is not a suggestion, it's a safety device). :)