  In this study, assuming the type-I 2HDM at SM-like scenario, observability of
heavy neutral CP-even and CP-odd Higgs bosons $H$ and $A$ at a linear collider
operating at $\sqrt{s}=1$ TeV is investigated through the signal process chain
$e^- e^+ \rightarrow A H \rightarrow ZHH$ where the $Z$ boson experiences a
leptonic ($e^-e^+$ or $\mu^-\mu^+$) decay and the $H$ Higgs boson is assumed to
decay into a di-photon. This signal process is motivated especially by the
clean signature which leptonic and photonic events can provide at colliders,
and also by the enhancement due to the charged Higgs-mediated contribution to
$H$ di-photon decay at large $\tan\beta$ values. Simulation is based on four
benchmark points according to which the Higgs mass $m_H$ ($m_A$) varies within
the range $150$-$300$ ($200$-$400$) GeV. Energy smearing of jets and photons
are performed, and momentum smearing is also applied to leptons. Results
indicate that, for all of the assumed benchmark points, the Higgs bosons $H$
and $A$ are observable with measurable masses, and with signals exceeding
$5\sigma$ at integrated luminosities $111$ and $201\,fb^{-1}$ respectively.
Such luminosities are easily accessible to future linear colliders.
