$\int (f * g)(x)\, h(x)\, dx = \int f(x)\,(g*h)(x)\, dx$

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I read the following convolution property in a proof of conservation of energy by Vlasov-Poisson. I tried to prove it without success.

$$\int (f * g)(x) \,h(x)\, dx = \int f(x)\,(g*h)(x) \,dx$$

With $(f*g)(x)=\int f(y)\,g(x-y)\,dy$

Is there someone who can help me to show this or give me a counter-example?