There is not much evidence for Zoroastrian influence on the Jewish transition to monotheism. By the time Judiasm was making the transition by the end of the exile, only certain, specific monarchs mention Ahura Mazda in their inscriptions, and it's worth pointing out that many referred to other deities as well. Cyrus, the first king of the Achaemenid Persian Empire, wrote the Cyrus Cylinder for the temple of Esagila at Babylon in which he explicitly acknowledges the existence of deities like Marduk, Nabu and Bel (1). Only Darius I, and specifically the Behistun inscription, refers to Ahura Mazda exclusively; Artaxerxes II refers to him in a triad with Anahita and Mithra. Furthermore, references to Ahura Mazda in this way are almost exclusively associated with royal inscriptions in the Achaemenid Empire; it's been theorised by a number of historians that Ahura Mazda was a royal cult, intended to be worshipped by the King of Persia and nobody else. It was not the official religion of the Empire; states did not function like that at the time, and the law of the Empire was whatever the King decided it was rather than being related to Zoroastrian texts. And we get into even muddier waters when we remind ourselves that the Persians are not the only Iranian speaking culture in this period.