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In this work we present a new computation of the lepton flavor violatingHiggs boson decays that are generated radiatively to one-loop from heavyright-handed neutrinos. We work within the context of the inverse seesaw modelwith three $\nu_R$ and three extra singlets $X$, but the results could begeneralized to other low scale seesaw models. The novelty of our computation isthat it uses a completely different method by means of the mass insertionapproximation which works with the electroweak interaction states instead ofthe usual 9 physical neutrino mass eigenstates of the inverse seesaw model.This method also allows us to write the analytical results explicitly in termsof the most relevant model parameters, that are the neutrino Yukawa couplingmatrix $Y_\nu$ and the right-handed mass matrix $M_R$, which is very convenientfor a phenomenological analysis. This $Y_\nu$ matrix, being genericallynondiagonal in flavor space, is the only responsible for the induced chargedlepton flavor violating processes of our interest. We perform the calculationof the decay amplitude up to order ${\cal O}(Y_\nu^2+Y_\nu^4)$. We also studynumerically the goodness of the mass insertion approximation results. In thelast part we present the computation of the relevant one-loop effective vertex$H\ell_i\ell_j$ for the lepton flavor violating Higgs decay which is derivedfrom a large $M_R$ mass expansion of the form factors. We believe that oursimple formula found for this effective vertex can be of interest for otherresearchers who wish to estimate the $H \to \ell_i \bar \ell_j$ rates in a fastway in terms of their own preferred input values for the relevant modelparameters $Y_\nu$ and $M_R$.

Effective lepton flavor violating $\boldsymbol{H\ell_i\ell_j}$ vertex from right-handed neutrinos within the mass insertion approximation