  The seesaw scale is a priori unknown. If the seesaw scale is low, one may
directly look for the new particles predicted by seesaw models. If the seesaw
scale is high, such an approach is unfeasible. We show that in some
supersymmetric seesaw models the large Yukawa couplings of high scale seesaw
models leave their fingerprints to Higgs-slepton couplings and that this can
result in decays of the type $\tilde{\nu}_{2}\rightarrow \tilde{\nu}_{1}h$ in
Type-I and Type-III seesaw models and $\tilde{\ell}^{\pm}_{2}\rightarrow
\tilde{\ell}^{\pm}_{1}h$ in the latter. Unfortunately the current exclusion
bounds make it impossible to see a significant signal even at the
High-Luminosity phase of the LHC. In this paper, we highlight that the
High-Energy phase of the LHC (with $\sqrt{s}=27$~TeV) could afford one with
some sensitivity to those in the single lepton channel.
