English translation: part-time work (for another employer)
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Explanation: 'moonlighting [for other employers]' is not an exact equivalent, but you may be able to get away with it :-)
Otherwise I suggest replacing the one Russian word with a lengthy English phrase such as "if the employee has concealed the fact that he holds other positions". The word совместительства just seems to repeat or sum up своего участия в органах управления других организаций