Is it permissible for one who wants to hasten his departure to appoint someone else to stone the jamarat, because it is difficult for him to reach the jamarat before sunset?

It is not permissible to appoint someone else to stone the jamarat unless you are unable to do it because of sickness or old age that makes it difficult to go to the jamarat.

Ibn Qudamah (may Allah have mercy on him) said: If a man is sick or detained, or has a valid excuse, it is permissible for him to appoint someone to stone the jamarat on his behalf."(Al-Mughni  3/427).

Shaykh Ibn Baz (may Allah have mercy on him) said: There is nothing wrong with appointing someone to stone the jamarat on behalf of one who is sick, or a woman who is unable to do it because she is pregnant, or heavy, or weak, and is not able to stone the jamarat."(Majmu‘ Fatawa Ibn Baz  17/301).

Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: It is not permissible for a woman or anyone else to appoint someone to stone the jamarat on her behalf, because stoning the jamarat is one of the actions of hajj, and Allah, may He be Blessed and exalted, says (interpretation of the meaning):

{And complete the hajj and ‘umrah for Allah} [al-Baqarah 2:196].

Hence the Prophet (blessings and peace of Allah be upon him) gave permission to the weak ones among his family to move on from Muzdalifah at night, so that they would reach Mina before the crowds and stone Jamrat al-‘Aqabah, but he did not give them permission to appoint someone to stone the jamarat on their behalf. Similarly, the Prophet (blessings and peace of Allah be upon him) gave permission to the camel herders to stone the jamarat one day and not the next, and he did not give them permission to appoint someone else to stone them on their behalf. This indicates that it is a must for the pilgrim to stone the jamarat himself."(Majmu‘ Fatawa Ibn ‘Uthaymin 23/107).

And he said: If the pilgrim is not able to stone the jamarat either because of old age, or sickness, or the pilgrim is a woman who is pregnant, or a woman or man who is blind and it is too difficult for them to do it, then in this case there is nothing wrong with appointing someone else to do it on their behalf, because of necessity."(Majmu ‘ Fatawa Ibn ‘Uthaymin  23/119).

As for hastening to depart [on 12^th Dhul-Hijjah], that is not an excuse, because there is enough time from noon until sunset to stone the jamarat, no matter where he is in Mina, as is the case for thousands of people nowadays, who may be at the far edges of Mina and in Muzdalifah, but they are able to stone the jamarat and hasten their departure.

If a person has no excuse that would keep him from stoning the jamarat, it is not permissible for him to appoint someone else to do it on his behalf.

And Allah knows best.