According to the suggestion for project prolongation, the significance of the experiments on searching for lepton number violations in the charged lepton sector µ→eγ and conversion of a muon to an electron in the nucleus field µN→eN was discussed. The status and prospects of the Mu2e (Fermilab) and MEG-II (PSI) experiments were considered, as well as the contribution of the DLNP staff members to the development of the electromagnetic calorimeter, muon veto system (Mu2e), drift chamber and data-taking system (MEG-II). The upcoming participation of the DLNP staff members in the Mu2e, COMET (J-PARC) and MEG-II experiments was also discussed.