The Iraqis secretly asked MATRA to integrate the R550 Magic 1 on MiG21 to turn the tide of the air war (MiG-21 were pretty obsolete compared with their Iranian counter parts). I would not say the Iraqis did it because the weapon was available. The Magic was a real game changer. The Iraqis new it, but they could not wait for the delivery of Mirage F1EQ (with their effective R550 / R530F combo).
By mid-April 1981, 24 MiG21-MF (2 squadrons) were using Magic.
Also, the use of Magic on MiG21 made Iraqis pilots more confident and aggressive. If I’m right, the Iranians lost 2 F-4E, 2 F-5E (those you were talking about) and 1 AH-1J in the following week, all destroyed by Magic missiles (according to the Iraqis at least). Of course that was a huge shock for the IRIAF, that’s also how it became aware of the use of Magic in May 1981.