$L$-function for $\mathrm{Sp}(4)\times\mathrm{GL}(2)$ via a non-unique model

In this paper we prove a conjecture of Ginzburg and Soudry on an integral representation for the $L$-function $L^S(s, π\times τ)$ attached to a pair $(π, τ)$ of irreducible automorphic cuspidal representations of $\mathrm{Sp}_4({\mathbb A})$ and $\mathrm{GL}_2({\mathbb A})$, which is derived from th