In this paper, we show the nondegeneracy of positive bubble solutions for generalized energy-critical Hartree equations (NLH) \(-\Delta {u}(x) - \alpha(N, \lambda)\int_{{\mathbb R}^{N}} {{u^{p}(y) \over \mid x - y \mid^{\lambda}}}dy \, u^{p - 1}(x) = 0, \quad x \in {{\mathbb R}^{N}},\) where \(N \geqslant 3, \, 0 < \lambda < N, \, p = {{2{N} - \lambda} \over {N - 2}}\) , and α(N, λ) is a normalized constant such that \(u(x) = {(1 + \mid x \mid^{2})}^{{- {N - 2} \over 2}}\) is a bubble solution of the equation (NLH). We extend the partial nondegeneracy results by Du and Yang (2019), Giacomoni et al. (2020) and Li et al. (2025) to the full range 0 < λ < N and completely solve the problem about the nondegeneracy of the positive bubble solutions of (NLH) by Gao et al. (2022) and Miao et al. (2015), which has lasted over a decade. The key observation is that the weighted pushforward map \({\cal S}_{\ast}\) is a one-to-one map between the null space of the linearized operator and the spherical harmonic function subspace \({{\cal H}_{1}^{N + 1}}\) of degree one by using the spherical harmonic decomposition, the stereographic projection \({\cal S}\) , and the Funk-Hecke formula, which is inspired by Frank and Lieb (2012).
