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Sort of, kind of, maybe; not really.
Weight lifting can increase muscle mass, primarily through becoming damaged (via weight lifting) and then sending out signals to the body to turn ingested proteins into new muscle tissue as a repair mechanism. Carbohydrates and fats are used as energy to fuel this process.
Weight lifting can also decrease fat mass, by using up body fat stores to fuel both this muscle building process and also using fat stores directly as fuel for the exercise that is needed to damage the muscle.
The technical, literal, direct conversion of fat into muscle.
Fat is comprised of triglycerides, which are molecules shaped like a capital E comprising a backbone and three chains of fatty acids (shown below). These chains are made up of carbon, hydrogen, and oxygen almost exclusively.
Muscle mass is made up of muscle tissue, glycogen, water, and some intra-muscular fat. The muscle tissue (the only tissue able to contract) is made up of chains of amino acids, which can be quite various in their structure. These chains contain nitrogen, and nitrogen is almost exclusively stored in the body as muscle (with some amino acids floating around).
It is impossible for fat to directly turn into muscle, since fat lacks the nitrogen and no mechanism exists in the body to reconstruct fat into amino acids. No evidence has surfaced implying that amino acids can be made in the body from anything other than other amino acids, a process known as transamination.
So although lifting weights can both build muscle and induce fat loss, these should be viewed as two separate results and not one being the result of another.