Finite Laplace transform representation for a Fox H-function kernel

Let $H_{q,p}^{p,0}\left(\xi\Big|^{(B_q,\beta_q)}_{(A_p,\alpha_p)}\right)$ denote the Fox H-function, and let $t$, $\xi$, and $\lambda$ be parameters with $0<t<1$ and $0<\xi<1$. Consider the function

$$\xi\mapsto \frac{1}{\xi(1-t\xi)^{\lambda}}H_{q,p}^{p,0}\left(\xi\Big|^{(B_q,\beta_q)}_{(A_p,\alpha_p)}\right).$$

Finite Laplace transform question. Can the finite Laplace transform of this function be expressed in terms of the Fox H-function?

The question is motivated by the preceding theorem and concerns an explicit special-function representation of the finite Laplace transform. The source does not state a resolution.