We measured absolute cross sections for neutron transfer channels populated in the 94Rb+208Pb binary reaction. Cross sections have been extracted identifying directly the lead isotopes with the high efficiency MINIBALL γ-ray array coupled to a particle detector combined with a radioactive 94Rb beam delivered at Elab=6.2 MeV/nucleon by the HIE-ISOLDE facility. We observed sizable cross sections in the neutron-rich mass region, where the heavy partner acquires neutrons. A fair agreement between the measured cross sections with those from GRAZING calculations gives confidence in the cross-section predictions of more neutron-rich nuclei produced via a larger number of transferred nucleons.