  The growth of large-scale structure, together with the geometrical
information of cosmic expansion history and cosmological distances, can be used
to obtain constraints on the spatial curvature of the universe that probes the
early universe physics, whereas modeling the nonlinear growth in a nonflat
universe is still challenging due to computational expense of simulations in a
high-dimensional cosmological parameter space. In this paper, we develop an
approximate method to compute the halo-matter and halo-auto power spectra for
nonflat $\Lambda$CDM model, from quantities representing the nonlinear
evolution of the corresponding flat $\Lambda$CDM model, based on the separate
universe (SU) method. By utilizing the fact that the growth response to
long-wavelength fluctuations (equivalently the curvature), $T_{\delta_{\rm
b}}(k)$, is approximated by the response to the Hubble parameter, $T_h(k)$, our
method allows one to estimate the nonlinear power spectra in a nonflat universe
efficiently from the power spectra of the flat universe. We use $N$-body
simulations to show that the estimator can provide the halo-matter (halo-auto)
power spectrum at $\sim 1\%$ ($\sim 2\%$ ) accuracy up to $k \simeq 3 (1) \, h
{\rm Mpc}^{-1}$ even for a model with large curvature $\Omega_K = \pm 0.1$.
Using the estimator we can extend the prediction of the existing emulators such
as Dark Emulator to nonflat models without degrading their accuracy. Since the
response to long-wavelength fluctuations is also a key quantity for estimating
the super sample covariance (SSC), we discuss that the approximate identity
$T_{\delta_{\rm b}}(k) \approx T_h(k)$ can be used to calculate the SSC terms
analytically.
