On-going measurements of the neutrinoless ββ decay are accompanied by the growing interest in computing the values of the associated nuclear matrix elements. In order to extract the neutrino mass from the potentially measured ββ half-lives one not only needs to know the values of the nuclear matrix elements but also the effective value of the weak axial-vector coupling constant gA since its value affects strongly the ββ half-lives. In order to gain knowledge of the possible quenching of gA in finite nuclei one can study, e.g., allowed Gamow-Teller β decays. A new promising tool to study the quenching are the measurements of ordinary muon capture transitions for which the range of momentum exchange, some 100 MeV, corresponds to the one of neutrinoless ββ decay.