Praise be to Allah.
Shaykh Ibn Baaz said:
It is permissible for the person who is acting on behalf of another to stone each of the three Jamaraat for himself first then on behalf of the other person, which is in one standing. He does not have to complete the stoning of the Jamaraat on his own behalf first and then go back and stone them on behalf of the other person, according to the more correct of the two scholarly opinions, because there is no evidence to that effect, and because that is too difficult. Allah says (interpretation of the meaning):
“and [Allah] has not laid upon you in religion any hardship” [al-Hajj 22:78]
And the Prophet (peace and blessings of Allah be upon him) said: “Be easy going and do not be harsh.” Narrated by al-Bukhaari, 96; Muslim, 1734.
And it was not narrated that the companions of the Messenger of Allah (peace and blessings of Allah be upon him) did that when they stoned the Jamaraat on behalf of their children and those who were unable to do it. If they had done that, it would have been narrated because there are reasons to narrated such a thing.
Fatawa Ibn Baaz, 16/86.
Shaykh Ibn ‘Uthaymeen said:
There is nothing wrong with a person stoning the Jamaraat on his own behalf, and on behalf of the person who has appointed him to do it for him, in one standing. He does not have to complete all three on his own behalf and then go back and stone them on behalf of the person who appointed him, because there is no evidence to suggest that this is obligatory.
Manaasik al-Hajj wa’l-‘Umrah, p. 95.