All perfect praise be to Allah, the Lord of the Worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Allah, the Exalted, says (what means): {Then whoever hastens [his departure] in two days—there is no sin upon him; and whoever delays [until the third]—there is no sin upon him—for him who fears Allaah.} [Quran 2:203]
Muslim jurists underlined that if a pilgrim hastens to depart Mina after spending two days only (from the three days of Tashreeq), then he should leave it before the sunset of the second day of Tashreeq so that he would actually leave it within two days. Whoever is in a hurry may depart Mina after midday and before sunset on the 12th; if he delays his departure and remains until sunset (of the second day of Tashreeq), the rule about staying in Mina for two days only does not apply in this case because the third day became due after the sunset in the second day (i.e. it is obligatory upon him to stay overnight and perform the rite of throwing the pebbles on the 13th of Thul Hijjah).
A group of the companions including the Commander of the Believers ‘Umar ibn Al-Khattaab and his son ‘Abdullaah held this opinion, which was also adopted by the majority of Muslim scholars.
If the pilgrim threw the pebbles after sunset (of the second day of Tashreeq), or even before it but he did not leave Mina until after sunset, then it is obligatory on him to spend that night, i.e. the eve of 13th of Thul-Hijah, at Mina and throw the pebbles at noon on the third day of Tashreeq, the 13th of Thul-Hijah, like was the case in the two previous days.
Hence, it is incumbent on the respected questioner to offer a sacrificial animal in Makkah and distribute its meat among the poor of the sanctuary only as expiation for failing to throw the pebbles on the third day of Tashreeq although, by remaining until sunset in Mina on the second day of Tashreeq, it has become obligatory on him. This is according to the opinion of the majority of Muslim jurists, who do not condition staying in Mina until the break of dawn for the obligation to throw the pebbles on the third day of Tashreeq.
You may authorize another person to slaughter the sacrificial animal (offered as expiation) on your behalf in Makkah. Moreover, it is also incumbent on you to feed a poor person with a mudd (0.75 liters) of foodstuff for not staying overnight on the third day of Tashreeq, the 13th of Thul-Hijjah, at Mina.
Allah Knows best.