Preheat oven to 350°F. Grease and line two 9-inch cake pans with parchment paper.
To make the cake, combine cake mix, pudding mix, flour and sugar in a large bowl and mix well. Add the oil and then add the eggs, mixing after each. Add the water and strawberries and mix until combined.
Divide the butter amongst the pans. Bake for 20-25 minutes until a toothpick inserted into the center comes out clean. Cool in the pans for 5 minutes and then turn out onto a wire rack and cool completely.
To make the frosting:
Cream together the cream cheese and butter until light and fluffy. Add the powdered sugar, in installments if necessary. Add the salt and vanilla and mix until combined.
Frost the cake and garnish with the shredded coconut and strawberries.