Kanev–Lange isomorphism conjecture for simply ramified $B_n$-coverings

Let $p:C\overset{\pi}{\longrightarrow}C'\overset{g}{\longrightarrow}\mathbb{P}^1$ be a simply ramified covering of type $B_n$. Let $P(C,C')$ be its Prym variety, let $P(X,\delta)$ be the associated Prym–Tyurin variety, and let $\mu:\widehat{P(C,C')}\to P(X,\delta)$ be the isogeny constructed from the covering. Kanev–Lange's $B_n$-covering conjecture. The isogeny $\mu:\widehat{P(C,C')}\to P(X,\delta)$ is an isomorphism. This is a specialization of the duality prediction to simply ramified $B_n$-coverings of $\mathbb{P}^1$; the supplied text does not establish it or state its resolution.