The 16-channel fast stretcher BaFPro module, originally developed for processing signals of Barium Fluoride scintillators, has been modified to make a high performing analog pulse-shape analysis of signals from the NE213 liquid scintillators of the EDEN neutron detector array. The module produces two Gaussian signals, whose amplitudes are proportional to the height of the fast component of the output light and to the total energy deposited into the scintillator, respectively. An in-beam test has been performed at INFN-LNS (Italy) demonstrating a low detection threshold, a good pulse-shape discrimination even at low energies and a wide dynamic range for the measurement of the neutrons energy.