Backyard drainage issues

I have a client with a sloped backyard that is getting washed out with every big rain. The water runs from the neighbors yards, under the fence and continues to take all of his topsoil. I have no clue about drainage issues and told him so, but he asked for help/advice.

What are the drainage options, or is there any way to either stop or divert the water. He is open to drainage or landscape features.

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Backyard drainage issues