This statement is true. As explained by an online magazine called Inverse, "Cooked carrots contain more beta-carotene than raw carrots, which is a substance called a carotenoid that the body converts into Vitamin A. This fat-soluble vitamin supports bone growth, vision, and immune system." The article by Inverse explains that cooking carrots with the skin will also double the antioxidant power that our body will receive from consuming them. There are also many other vegetables that are more nutritious when they are cooked such as bell peppers, tomatoes, and spinach.
Source: inverse.com/innovation/vegetables-healthier-when-cooked