Nonvanishing conjecture for distinct multiple zeta-star values

Let $s$ satisfy $\operatorname{Re}(s)>1$, and let $(k_1,\ldots,k_p)$ and $(l_1,\ldots,l_q)$ be distinct finite sequences of positive integers. Write $H_s^\star(k_1,\ldots,k_p)$ for the corresponding multiple zeta-star value. Nonvanishing conjecture. For $(k_1,\ldots,k_p)\neq(l_1,\ldots,l_q)$, one has

$$H_s^\star(k_1,\ldots,k_p)-H_s^\star(l_1,\ldots,l_q)\neq 0.$$

This asserts that distinct finite sequences give distinct multiple zeta-star values in the half-plane $\operatorname{Re}(s)>1$. If true, it would provide uniqueness for the finite zeta-star correspondence and support the broader program of encoding sequences by these values; the supplied context does not state that it has been proved or disproved.