In the present work, we consider a magnetization moment recovery problem, that is finding integral of the vector function (over its compact support) whose divergence constitutes a source term in the Poisson equation. We outline derivation of explicit asymptotic formulas for estimation of the net magnetization moment vector of the sample in terms of partial data for the vertical component of the magnetic field measured in the plane above it. For this purpose, two methods have been developed: the first one is based on approximate projections onto spherical harmonics in Kelvin domain while the second stems from analysis in Fourier domain following asymptotic continuation of the data. Recovery results obtained by both methods agree and are illustrated numerically by plotting formulas for net moment components with respect to the size of the measurement area.