  The \textit{axial} electromagnetic (EM) perturbations of the black hole (BH)
solutions in general relativity coupled to nonlinear electrodynamics (NED) were
studied for both electrically and magnetically charged BHs, assuming that the
EM perturbations do not alter the spacetime geometry in our preceding paper
[Phys. Rev. D 97, 084058 (2018)]. Here, as a continuation of that work, the
formalism for the \textit{polar} EM perturbations of the BHs in general
relativity coupled to the NED is presented. We show that the quasinormal modes
(QNMs) spectra of polar EM perturbations of the electrically and magnetically
charged BHs in the NED are not isospectral, contrary to the case of the
standard Reissner-Nordstr\"{o}m BHs in the classical linear electrodynamics. It
is shown by the detailed study of QNMs properties in the eikonal approximation
that the EM perturbations can be a powerful tool to confirm that in the NED
light ray does not follow the null geodesics of the spacetime. By specifying
the NED model and comparing axial and polar EM perturbations of the
electrically and magnetically charged BHs, it is shown that QNM spectra of the
axial EM perturbations of magnetically (electrically) charged BH and polar EM
perturbations of the electrically (magnetically) charged BH are isospectral,
i.e., $\omega_{mag}^{ax}\approx\omega_{el}^{pol}$
($\omega_{mag}^{pol}\approx\omega_{el}^{ax}$).
