This woman must observe the ‘iddah after having been divorced by her husband, and she should start counting the ‘iddah from the time when she received word of the divorce.
Shaykh Ibn Baaz (may Allaah have mercy on him) was asked about a man who stayed away from his wife and was travelling for twenty years, after which he sent word to her of divorce. This woman wants to get married – does she have to observe the ‘iddah? Because her husband has been away from her for twenty years and has not touched her. Is the purpose of the ‘iddah to establish that there is no pregnancy, or is it for another purpose?
He replied: If the matter is as described, there is no doubt that she must observe the ‘iddah, because the ‘iddah can only begin after a divorce has taken place, even if the husband has been away from the woman who is now divorced, because Allaah says (interpretation of the meaning):
“And divorced women shall wait (as regards their marriage) for three menstrual periods”
With regard to the reason behind that, there is a valuable essay on this topic by the great scholar Ibn al-Qayyim (may Allaah have mercy on him) in I’laam al-Muwaqqi’een. He stated that the reason is not only to establish that there is no pregnancy, rather there are other reasons. Hence a woman whose husband has died must also observe the ‘iddah even if the marriage was not consummated, and even if she is too young to become pregnant or is past the age of child-bearing. Thus it is known that there are reasons why Allaah has enjoined the ‘iddah other than to establish that there is no pregnancy. But if the woman whom you mention gave him money and he divorced her in return, then in that case it is khula’ and there is evidence from the Prophet (peace and blessings of Allaah be upon him) to suggest that in the case of a woman who is divorced by means of khula’, one menstrual cycle is sufficient as ‘iddah. ‘Uthmaan ibn ‘Affaan (may Allaah be pleased with him) and a number of the earlier and later generations issued fatwas to that effect, and this view was favoured by Shaykh al-Islam Ibn Taymiyah and his student Ibn al-Qayyim (may Allaah have mercy on them both). And this is the correct view, in sha Allaah, especially if there is a need for that, if there is the fear that the opportunity to marry a compatible man may be lost if he is asked to wait until three menstrual cycles (or three months in the case of a postmenopausal woman) have passed. I ask Allaah to help us, you and all our Muslim brothers to understand His religion properly and to adhere steadfastly to it, for He is Most Generous and Kind.
End quote from Majmoo’ Fataawa al-Shaykh Ibn Baaz (22/172)
And Allaah knows best.