  We report the theoretical investigation of the suppression of magnetic
systematic effects in HfF$^+$ cation for the experiment to search for the
electron electric dipole moment. The g-factors for $J = 1$, $F=3/2$,
$|M_F|=3/2$ hyperfine levels of the $^3\Delta_1$ state are calculated as
functions of the external electric field. The lowest value for the difference
between the g-factors of $\Omega$-doublet levels, $\Delta g = 3 \times
10^{-6}$, is attained at the electric field 7 V/cm. The body-fixed g-factor,
$G_{\parallel}$, was obtained both within the electronic structure calculations
and with our fit of the experimental data from [H. Loh, K. C. Cossel, M. C.
Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science {\bf
342}, 1220 (2013)]. For the electronic structure calculations we used a
combined scheme to perform correlation calculations of HfF$^+$ which includes
both the direct 4-component all-electron and generalized relativistic effective
core potential approaches. The electron correlation effects were treated using
the coupled cluster methods. The calculated value $G_{\parallel}=0.0115$ agrees
very well with the $G_{\parallel}=0.0118$ obtained in the our fitting
procedure. The calculated value $D_{\parallel}=-1.53$ a.u. of the molecule
frame dipole moment (with the origin in the center of mass) is in agreement
with the experimental value $D_{\parallel}=-1.54(1)$ a.u. [H. Loh, Ph.D.
thesis, Massachusetts Institute of Technology (2006)].
