Zoroastrianism is routinely credited with supplying Judaism, and through it Christianity and Islam, with a package of ideas: a named adversary of God, ranks of angels and demons, bodily resurrection, a judgement after death, a saviour at the end of history, and a renewed world. The Jewish material that most resembles this appears after the Achaemenid period, when Judaea was under Persian rule and Jewish communities were living in Iran, so the opportunity for contact is not in doubt.
What is in doubt is the direction and the proof. The Zoroastrian texts that set the scheme out most fully, the Bundahishn and other Pahlavi works, were written down in the Islamic period, many centuries after the Jewish texts they are said to have influenced. The Avesta itself was transmitted orally for a very long time before being written, so its contents cannot be dated the way a manuscript can. Scholars who argue for influence reply that Iranian oral transmission was conservative and that the Gathas already contain the essentials. Scholars who resist it answer that arguing from an undated source to a dated one inverts the normal method, and that comparable ideas developed inside Second Temple Judaism for reasons of its own.
Both positions are held by serious specialists in the field, and the disagreement will not be settled by argument alone. It would take datable Iranian evidence from the relevant centuries, which does not at present exist. The honest statement is that the resemblance is real, the contact is real, and the dependence is unproven in either direction.
A separate and better evidenced line of transmission runs the other way. Greek and Roman writers turned Zoroaster into a legendary sage and attached astrological and magical writings to his name that have nothing to do with Iranian religion. The Latin magus, from the Iranian priestly title, entered European languages carrying that freight, and the magi of the Christmas narrative are a trace of the same reputation. Much of what Europe long believed about Zoroastrianism came from this literature rather than from Zoroastrians, and the Avesta became available in Europe only after Anquetil-Duperron travelled to India in the 1750s to obtain it.