Charles: Correct, thanks for jumpstarting my memory. And I don't believe the Soviets confiscated it later and issued him a new one. If so then where did this come from?
As you can see if you go through it, it has 1959 stamps on it when he first arrived. And then it has 1962 stamps/dates - one German - when he left. So it seems logical to conclude that he didn't turn in his older 1959 passport and then was given a new one by the Soviets when he left. It has both 1959 and 1962 dates. This is clearly the passport he had when he arrived. And given back when he left.
If this is the passport then as you can see (page #7) there are Soviet "marks" on it. If he had this then it seems to me that it is probably (likely? possibly?) the passport that he showed the Australian women.