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Sequential two-photon ionization is a process that is experimentally accessible due to the use of new free-electron laser sources for excitation. For the prototypical rare Ar gas atoms, a photoelectron spectrum (PES) corresponding to the second step of the sequential two-photon double ionization (2PDIII) at a photon excitation energy of 65.3 eV was studied theoretically with a focus on the consequences of electron correlations in the considered process. The calculation predicts many intense lines at low photoelectron energies, which cannot be explained on the basis of a one-electron approximation. The processes that lead to the appearance of these lines include many-electron correlations, either in the first or second step of photoionization. A significant fraction of the intensity of the low-energy part of PES is associated with the Auger decay of the excited states formed at the second step of 2PDI. The shape of the low-energy part of the 2PDIII PES is expected to be dependent on both the energy of photon excitations and the flux of the exciting beam.