WI: Divided Iran post-WWII

The Anglo-Soviet Invasion of Iran in 1941 was fueled in part by fears of Reza Shah Pahlavi being pro-German (which was false, Reza wanted to remain neutral), but also by the two factions competing desires to increase their influence over Iran.

Now assuming, that with the increasing divide between the Western Allies and the Soviets lead to a worst-case scenario for Iran, that the Soviets and the British (along with the United States) effectively split Iran in two (or maybe three or four, depending on if Southern Azerbaijan & Mahabad/Kurdistan still is a thing), between a Communist North and British-backed South (either under Mohammed Reza or a Qajar Shah). If such a split happens, how would it effect Cold War politics in the Middle East?
 
This would require a much more antagonistic realtionship between the USSR and the allies seeing as in the Tehran conference they were both committed to a unified Iran as part of the allies.

So a pre invasion pod is probably required.
 
Americans find out the Soviets had been feeding intel to the Japanese and that the Manhattan Project had been infiltrated, along with a more bellicose VP for FDR should do the trick.
 
Okay, so in an alternative case, what if Stalin for some reason or another, decides not to abide by the Tehran Conference agreement, and decides to just integrate its portion of the Persian corridor (or part of it, mainly the Turkmen Sahra & Iranian Azerbaijan). This after all plays into consideration, the 1946 Iran Crisis, when the Soviets did not leave Iran on the agreed date, citing Soviet security concerns.
 
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