Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.

 

The iddaH starts after the divorce is finalized either verbally or in paper depending on each court in each country. So to that I suggest to ask the judge where the divorce is to be processed.

 

Now, you did not specify if they consummated the marriage or not. If no consummation of marriage took place, just paper like Kitab then no iddat is required and only half Mahr should be returned. If they did have intimate relation, then full Mahr is required and the iddah is 3 menstrual periods from the divorce time.
Almighty Allah knows best.