What is the sharia ruling concerning a pilgrim who forgets to throw the Jamrah of Al-‘Aqabah on the day of 'Eed (the 10th day of Thul-Hijjah) on behalf of his sick wife?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Whoever forgets to throw the Jamrah of Al-‘Aqabah and does not do it later during the days of Tashreeq (the 11th, 12th and 13th days of Thul-Hijjah) has to slaughter a sheep in the precincts of Mecca. But if he does it later, he is not liable for anything because throwing the pebbles is valid during all the days of Mina. In Al-Insaf, Al-Mardawi said: 

If he delays all the incidents of throwing the pebbles; i.e. Jamrat Al-‘Aqabah, which is to be thrown on the Day of Nahr, as well as the pebbles to be thrown in the days of Tashreeq,  until the last day of the days of Tashreeq, then his action is valid according to the consensus of the scholars. It is also considered to be done at the prescribed fixed time according to the soundest opinion adopted by the Hanbali scholars.

In Tuhfat Al-Muhtaj, Ibn Hajar Al-Haythami said:

If a pilgrim does not throw the pebbles of the day of 'Eed (the 10th day of Thul-Hijjah) or of the next days, deliberately or forgetfully, then he can do it during the other days. It is also considered to be done at the prescribed, fixed time according to the soundest opinion. As evidence, the Prophet, sallallaahu ‘alayhi wa sallam, allowed shepherds to do so. Had it not been valid to throw the pebbles at any time of these days (i.e. the days of Tashreeq), then there would have been no difference between those who had excuses and others, such as in standing on ‘Arafah and staying the night at Muzdalifah. When the Prophet, sallallaahu ‘alayhi wa sallam, allowed those who had excuses to throw at anytime, it necessarily included the permissibility for others to do the same.

Allaah Knows best.