It is actually very rare, and very unlikely, for protein to actually be converted into fat.
In reality, what happens is that when excess calories are consumed, whether from protein, fat, or carbohydrates, more of our dietary fat is stored as body fat.
If we eat excess protein, we oxidize more protein and less dietary fat (since we have a far greater storage capacity for fat than protein), and therefore store more of our dietary fat as body fat.
Same goes for eating excess carbs. Some carbs can be converted to body fat, but for the most part if we eat excess carbs, we oxidize more carbs and less dietary fat, causing more dietary fat to be stored as body fat.