  We demonstrate that complex point transformations can be used to construct
non-Hermitian first integrals, time-dependent Dyson maps and metric operators
for non-Hermitian quantum systems. Initially we identify a point transformation
as a map from an exactly solvable time-independent system to an explicitly
time-dependent non-Hermitian Hamiltonian system. Subsequently we employ the
point transformation to construct the non-Hermitian time-dependent invariant
for the latter system. Exploiting the fact that this invariant is
pseudo-Hermitian, we construct a corresponding Dyson map as the adjoint action
from a non-Hermitian to a Hermitian invariant, thus obtaining solutions to the
time-dependent Dyson and time-dependent quasi-Hermiticity equation together
with solutions to the corresponding time-dependent Schr\"odinger equation.
