This note is a reply to the paper (arXiv:1801.0559v2): " The gauge-invariant Lagrangian, the Power-Zienau-Woolley picture, and the choices of field momenta in nonrelativistic quantum electrodynamics" by G. Kónya, et al. See also our first reply (arXiv:1804.07472v1) in response to their initial comment "The equivalence of the Power-Zineau-Woolley picture and the Poincaré gauge from the very first principles " ( arXiv:1801.05590v1) ————————————– In a recent paper, we have shown that the Power-Zienau-Woolley Hamiltonian does not derived from the minimal-coupling hamiltonian with the help of a gauge transformation. This result has been challenged by G. Kónya and al. They first claim an error [arXiv:1801.05590v1] followed by a subsequent allegation that the Power-Zienau-Woolley hamiltonian can be derived starting from the electromagnetic action. We do not share their conclusions and show in two back-to-back replies [arXiv:1804.07472v1 followed by this note] that their successive statements are not correct.