  Symmetry plays a fundamentally important role in physics. In this work, we
find a conservation law, $S^{\dagger}(H_{c}^{\dagger})S(H_{c})=I$, which is
valid for any non-Hermitian scattering center $H_c$. As a result, the
reflections and transmissions of a non-Hermitian system $\left\{ r,t\right\}$
and its Hermitian conjugation system $\left\{ \bar{r},\bar{t}\right\} $ satisfy
the conservation law $\bar{r}^{\ast}r+\bar{t}^{\ast}t=1$, instead of the energy
conservation law that applies to incoming and outgoing waves in a Hermitian
system. Consequently, the pseudo-Hermiticity of a non-Hermitian system ensures
an energy-difference conservation. Furthermore, we demonstrate that the
energy-difference conservation is respectively valid and invalid in two
prototypical anti-$\mathcal{PT}$-symmetric systems, where the energy-difference
conservation is protected by the pseudo-Hermiticity. Our findings provide
profound insight into the conservation law, the pseudo-Hermiticity, and the
anti-$\mathcal{PT}$-symmetry in non-Hermitian systems.
