I refer to the paper ["Normal Subgroups in the Cremona Group"][1]. In the last paragraph of the proof of proposition 5.13, the author wrote the following: "Assume now that $h\in \text{Bir}(X)$ preserves the axis of $g_\ast$. Then $h_\ast [D']$ is an ample class." Here $[D']$ is an ample class in $N^1(X)\cap V_g$. May I ask how is the ampleness of $h_\ast[D']$ deduced? 

[1]: https://link.springer.com/content/pdf/10.1007/s11511-013-0090-1.pdf