  We prove an extension of the homology version of the Hofer-Zehnder conjecture
proved by Shelukhin to the weighted projective spaces which are symplectic
orbifolds. In particular, we prove that if the number of fixed points counted
with their isotropy order as multiplicity of a non-degenerate Hamiltonian
diffeomorphism of such a space is larger than the minimum number possible, then
there are infinitely many periodic points.
