Linarite, PbCuSO4(OH)2, is a natural mineral which has been shown to display a rich and complex phase diagram in applied fields up to 10 T for temperatures below 2.8 K. Our neutron diffraction measurements have revealed an incommensurate helical ground state in this highly frustrated material. In order to determine the field and temperature dependence of the magnetic moment in phase IV and V an elastic neutron diffraction measurement has been carried out recently for the low temperature (down to 50 mK) and the high field regime (up to 9.4 T) of the magnetic phase diagram. This way, the field and temperature dependence of the magnetic moment could be derived. Only, for an intermediate temperature range 1.2 - 1.8 K, because of thermal instabilities, matching of the D10 data with previous E2 data produced some ambiguity. Therefore, we would like to more accurately investigate the overlap area (1.2 - 1.8 K, up to 6.5 T) of the phase diagram via elastic neutron diffraction on E2.