If you ask the Iranians, they say they’ve shot down scores of Iraqi jets with the Phoenix.
Iranians say lots of things.
Their F-14's and their Phoenix missiles were supposedly sabotaged after the Revolution.
In any case, it would be really, really hard to keep up the maintenance of them without access to batteries and spare parts.
Iran was supplied with the original analog AIM-54 version of the missile that was replaced with a digital version shortly after the revolution making acquisition of spares even harder.
Whatever shoot downs they had in the 80's Iran-Iraq war would have been with AIM-7 Sparrows (good luck with that) or AIM-9 Sidewinders.