Do you have a source showing that he was imprisoned in Iraq? Wikipedia suggests he was there freely
https://en.wikipedia.org/wiki/Ruhollah_Khomeini%27s_life_in_...
He was imprisoned in Iran, then went to Turkey and from there to Iraq iirc, but it is long ago, so I suspect the GP meant after he was arrested by the Shah.
He was imprisoned in Iran, then went to Turkey and from there to Iraq iirc, but it is long ago, so I suspect the GP meant after he was arrested by the Shah.