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We construct an additional independent integral of motion for a class ofthree dimensional minimally superintegrable systems with constant magneticfield. 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 thepresent paper we demonstrate that it is maximally superintegrable. Depending onthe values of the parameters of the system, the newly found integral can be ofarbitrarily high polynomial order in momenta.

An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals