  We construct an additional independent integral of motion for a class of
three dimensional minimally superintegrable systems with constant magnetic
field. This class was introduced in [J. Phys. A: Math. Theor. 50 (2017),
245202, 24 pages] and it is known to possess periodic closed orbits. In the
present paper we demonstrate that it is maximally superintegrable. Depending on
the values of the parameters of the system, the newly found integral can be of
arbitrarily high polynomial order in momenta.
