= Solution
Use fractional <coordinates> and the <structure factor> convention
$$
F(\mathbf h)=\sum_j f_j e^{2\pi i\mathbf h\cdot\mathbf r_j},\qquad I(\mathbf h)\propto |F(\mathbf h)|^2.
$$
For real <atomic scattering factors>, $F(-\mathbf h)=F(\mathbf h)^*$, immediately proving <Friedel's law>. If an inversion centre is chosen as origin, each site at $\mathbf r_j$ has an identical partner at $-\mathbf r_j$, with the same possibly complex <atomic scattering factor>. Each pair contributes $2f_j\cos(2\pi\mathbf h\cdot\mathbf r_j)$; sites fixed by inversion modulo a <lattice translation> also have even phase factors at reciprocal-lattice vectors. Hence
$$
\boxed{F(-\mathbf h)=F(\mathbf h),\qquad I(-\mathbf h)=I(\mathbf h)}
$$
even for scalar <anomalous X-ray scattering> in a centrosymmetric structure. This last equality is an equality of amplitudes, not generally complex conjugacy.
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