Your body cannot convert fat to muscle. Muscle and fat are 2 completely different types of tissues, and one doesn't just magically turn into the other. Gaining muscle has little effect on your body fat percentage. Sure, you'll burn a little more fat by having more muscle but nothing significant. The only way to lose fat is through cardio training, like running, cycling etc.
'Converting fat to muscle' is kind of an expression. Nobody says that and means 'I'm drinking a smoothie that chemically alters the body's fat and turns it into muscle.' What they mean is, "I'm not actually losing weight; I'm losing fat, but I'm also building muscle, so even though I'm losing fat, my body weight isn't changing much. Really, it's kind of like I'm converting my weight from fat to muscle, as I lose fat and gain muscle."
Also, for the record, cardio routines are NOT the only way to burn fat. They are simply the most efficient. The body burns more calories depending on the heart rate - for this reason, cardio routines are very effective, because cardio is designed to keep the heart rate in an ideal range. But, literally anything that increases the heart rate, also increases the rate at which the body burns calories. So, for instance, walking. Taking a leisurely walk isn't exactly the best way to burn fat, but you WILL burn more fat by taking a leisurely walk than by taking a nap. And a light jog will be more effective than a leisurely walk, and a run will be more effective than a light jog, and et cetera. Cardio is he most efficient way to burn fat, but yes, you can burn some fat by weight lifting.
EDIT: Sorry for the rant. It's just, I've heard a lot of people complaining about not losing weight from weight training, so I've learned: they don't lose weight because they are gaining muscle, and their weight doesn't go up, either, because they're also burning fat.