  We mainly show the nondegeneracy of positive bubble solutions for generalized
energy-critical Hartree equations (NLH) \begin{equation*}
  -{\Delta u}\sts{x}
  -{\bm\alpha}\sts{N,\lambda}
  \int_{\R^N}
  { \frac{ u^{p}\sts{y}}{\pabs{\,x-y\,}{\lambda}} }\diff{y}\,
  u^{p-1}\sts{x}
  =0,\quad x\in \R^N \end{equation*} where $u(x)$ is a real-valued function,
$N\geq 3$, $0<\lambda<N$, $p=\frac{2N-\lambda}{N-2}$ and
${\bm\alpha}\sts{N,\lambda}$ is a normalized constant. It generalizes the
nondegeneracy results of positive bubble solutions in \cite{DY2019dcds,
GWY2020na, LTX2021} to the full range $0<\lambda<N$, and confirms an open
nondegeneracy problem in \cite{GMYZ2022cvpde}. The key observation is that the
weighted pushforward map $\mathcal{S}_*$ related to the stereographic
projection $\mathcal{S}$ is one-to-one map between the null space of the
linearized operator and the spherical harmonic function subspace
$\mathcal{H}_1^{N+1}$ of order one.
