Cats with dry and dull fur can eat the following foods:

Cooked egg yolks: Cooked egg yolks are rich in lecithin, which can improve hair loss, promote hair growth, and make newly grown hair shiny and lustrous.
Carrots: Carrots are rich in vitamins, which can make hair shiny and smooth, and can also promote digestion.
Dairy products: Dairy products contain high-quality protein and are rich in calcium, vitamins and trace elements such as copper and zinc, which can supplement the nutrients needed by cats.
Olive oil: Olive oil is rich in unsaturated fatty acids, which can make hair shiny and improve its quality.
Salmon: Salmon is rich in unsaturated fatty acids Omega-6 and Omega-3, making it an excellent food for healthy fur.