You can't get access to the texture from the widget directly.
You could get it through the texture manager, but you will have to know the filename of the texture. So this method works if you want access to a specific texture, but can't be used to get the same texture as a widget without knowing what it was loaded with. The "(0, 0, 300, 25)" in this code is the part of the image to load, in this case the child window title bar.
tgui::Texture temp;
tgui::TGUI_TextureManager.getTexture("TGUI/widgets/Black.conf", temp, sf::IntRect(0, 0, 300, 25));
sf::Texture& texture = temp.data->texture; // you can assign this to a sprite
sf::Sprite& sprite = temp.sprite; // or just use the sprite that already exists
(you will actually have to store the 'temp' variable, because you have to call tgui::TGUI_TextureManager.removeTexture(temp) to release the texture again, otherwise you will create a memory leak)
The only advantage you get from using the above code instead of the following is that the texture manager will reuse the same texture if it was already loaded.
sf::Texture texture;
texture.loadFromFile("TGUI/widgets/Black.conf", sf::IntRect(0, 0, 300, 25));
sf::Sprite sprite(texture);
But why would you want to access the textures that the widgets use?