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

We prove a conjecture of Ginzburg and Soudry (2020 IMRN) on an integral representation for the tensor product partial L-function for $\mathrm{Sp}(4) \times \mathrm{GL}(2)$ which is derived from the twisted doubling method of Cai, Friedberg, Ginzburg, and Kaplan. We show that the integral unfolds to a non-unique model and analyze it using the New Way method of Piatetski-Shapiro and Rallis.