Details of the German effort come from ‘European Axis Signals Intelligence' vol 6 - The foreign office cryptanalytic section and vol1 - Synopsis.
From EASI vol 6 p29 :
The group head for Iran, Afghanistan and Arabic states was Dr Benzing. According to him all Iranian systems were read.
Iran (Persia): Dr Benzing stated that all the Iranian systems were read. The Iranians used three letter, 12.000-13.000 group, one-part or reverse alphabetic, enciphered code books.
From EASI vol1:
Also from TICOM I-22 'Interrogation of German Cryptographers of Pers Z S Department of the Auswaertiges Amt', p20
166. All the Persian systems were read. They used a three letter book with substitution tables, which often changed. The Persians however always indicated in clear which table was in use.
The Germans were not the only ones who were reading Iranian codes. EASI vol1 mentions that the United States Army Security Agency (predecessor of the NSA) had acquired copies of the codes and most ‘keys’ were read.