  A non-Hermitian region connected to semi-infinite Hermitian lattices acts
either as a source or as a sink and the probability current is not conserved in
a scattering typically. Even a $\mathcal{P}\mathcal{T}$-symmetric region that
contains both a source and a sink does not lead to current conservation
plainly. We propose a model and study the scattering across a non-Hermitian
$\mathcal{P}\mathcal{T}$-symmetric two-level quantum dot~(QD) connected to two
semi-infinite one-dimensional lattices in a special way so that the probability
current is conserved. Aharonov-Bohm type phases are included in the model,
which arise from magnetic fluxes ($\hbar\phi_{L} /e,~\hbar\phi_{R} /e$) through
two loops in the system. We show that when $\phi_L=\phi_R$, the probability
current is conserved. We find that the transmission across the QD can be
perfect in the $\mathcal{P}\mathcal{T}$-unbroken phase (corresponding to real
eigenenergies of the isolated QD) whereas the transmission is never perfect in
the $\mathcal{P}\mathcal{T}$-broken phase (corresponding to purely imaginary
eigenenergies of the QD). The two transmission peaks have the same width only
for special values of the fluxes (being odd multiples of $\pi\hbar/2e$). In the
broken phase, the transmission peak is surprisingly not at zero energy. We give
an insight into this feature through a four-site toy model. We extend the model
to a $\mathcal{P}\mathcal{T}$-symmetric ladder connected to two semi-infinite
lattices. We show that the transmission is perfect in unbroken phase of the
ladder due to Fabry-P\'erot type interference, that can be controlled by tuning
the chemical potential. In the broken phase of the ladder, the transmission is
substantially suppressed.
