# Birational maps mapping ample class to ample class?

I refer to the paper "Normal Subgroups in the Cremona Group". 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?