Non-isogenous superelliptic jacobians II

Let $\mathrm{\ell }$ be an odd prime and $K$ a field of characteristic different from $\mathrm{\ell }$. Let $\bar{K}$ be an algebraic closure of $K$. Assume that $K$ contains a primitive $\mathrm{\ell }$th root of unity. Let $n\mathrm{\ne }\mathrm{\ell }$ be another odd prime. Let $f(x)$ and $h(x)$ be degree $n$ polynomials with coefficients in $K$ and without repeated roots. Let us consider superelliptic curves $C_{f,\mathrm{\ell }}:y^{\mathrm{\ell }}=f(x)$ and $C_{h,\mathrm{\ell }}:y^{\mathrm{\ell }}=h(x)$ of genus $(n-1)(\mathrm{\ell }-1)\mathrm{/}2$, and their jacobians $J^{(f,\mathrm{\ell })}$ and $J^{(h,\mathrm{\ell })}$, which are $(n-1)(\mathrm{\ell }-1)\mathrm{/}2$-dimensional abelian varieties over $\bar{K}$. Suppose that one of the polynomials is irreducible and the other reducible over $K$. We prove that if $J^{(f,\mathrm{\ell })}$ and $J^{(h,\mathrm{\ell })}$ are isogenous over $\bar{K}$ then both endomorphism algebras ${\mathrm{E}\mathrm{n}\mathrm{d}}^0(J^{(f,\mathrm{\ell })})$ and ${\mathrm{E}\mathrm{n}\mathrm{d}}^0(J^{(h,\mathrm{\ell })})$ contain an invertible element of multiplicative order $n$.