  Mixed spin-(1/2,1/2,1) trimer with two different Land\'{e} g-factors and two
different exchange couplings is considered. The main feature of the model is
non-conserving magnetization. The Hamiltonian of the system is diagonalized
analytically. We presented a detailed analysis of the ground state properties,
revealing several possible ground state phase diagrams and magnetization
profiles. The main focus is on how non-conserving magnetization affects quantum
entanglement. We have found that non-conserving magnetization can bring to the
continuous dependence of the entanglement quantifying parameter (negativity) on
magnetic field within the same eigenstate, while for the case of uniform
$g$-factors it is a constant. The main result is an essential enhancement of
the entanglement in case of uniform couplings for one pair of spins caused by
an arbitrary small difference in the values of $g$-factors. This enhancement is
robust and brings to almost 7-fold increasing of the negativity. We have also
found weakening of entanglement for other cases. Thus, non-conserving
magnetization offers a broad opportunity to manipulate the entanglement by
means of magnetic field.
