Bukhari

Hadith Commentary:
His name was Ali bin Umayyah.
Further explanation regarding him will come in the mention of the Battle of Badr.
The connection of the chapter heading to this hadith is derived as follows: Umayyah was a disbeliever at war (kafir harbi).
And he resided in the abode of war (dar al-harb), that is, Makkah.
Abdur Rahman (radi Allahu anhu) was a Muslim, but he appointed him as his agent (wakil), and when it was permissible to appoint him as an agent in the abode of war, then if he comes to the abode of Islam (dar al-Islam) under a guarantee of safety (aman), it will be even more permissible to appoint him as an agent.
Ibn al-Mundhir said that there is consensus among the scholars on this.
There is no disagreement that a disbeliever at war (kafir harbi) may appoint a Muslim as his agent, or a Muslim may appoint a disbeliever at war as his agent—both are valid.
Bilal (radi Allahu anhu) was formerly a slave of this very Umayyah.
He inflicted countless hardships upon him.
So that he might turn away from Islam.
But Bilal (radi Allahu anhu) remained steadfast until the end, until the Battle of Badr took place.
In that battle, when Bilal (radi Allahu anhu) saw this accursed man, he called the Ansar.
So that, with their help, he might kill him.
But since there was correspondence between Abdur Rahman bin Awf (radi Allahu anhu) and this accursed Umayyah, Abdur Rahman bin Awf (radi Allahu anhu) tried to save him.
And he pushed his son towards the Ansar.
So that the Ansar would be occupied with him.
But the Ansar killed his son and then wanted to attack Umayyah, so Abdur Rahman (radi Allahu anhu) lay over him in order to save him in this way.
But in the end, the Ansar killed him.
And in this skirmish, Abdur Rahman (radi Allahu anhu)'s foot was also injured.
The marks of which he used to show later.
Hafiz Ibn Hajar (rahimahullah) says regarding this hadith:
"And the reason for deriving the chapter heading from this hadith is that Abdur Rahman bin Awf, who was a Muslim in the abode of Islam, entrusted his affairs to Umayyah bin Khalaf, who was a disbeliever in the abode of war, and it is apparent that the Prophet (sallallahu alayhi wa sallam) was aware of this and did not object to it. And Ibn al-Mundhir said: There is no disagreement regarding the permissibility of a Muslim appointing a harbi (disbeliever at war) who is under a guarantee of safety (musta'man) as his agent, or a harbi musta'man appointing a Muslim as his agent."
That is, the connection of the chapter heading to this hadith is established in this way: Abdur Rahman bin Awf (radi Allahu anhu), who was a Muslim and in the abode of Islam, entrusted his wealth in the abode of war to Umayyah bin Khalaf, a disbeliever, and it is evident that this incident was known to the Prophet (sallallahu alayhi wa sallam).
But the Prophet (sallallahu alayhi wa sallam) did not object to it.
Therefore, Ibn al-Mundhir has said that there is no disagreement regarding the permissibility of a Muslim appointing a trustworthy harbi disbeliever as his agent, or a harbi disbeliever appointing a trustworthy Muslim as his agent.

Hadith Commentary:
(1)
Abdur-Rahman ibn Awf (radi Allahu anhu) was a Muslim, residing in the abode of Islam, the blessed city of Madinah, while Umayyah ibn Khalaf was a disbeliever, residing in the abode of war. There was a mutual agreement between the two that each would look after the rights and interests of the other in their respective territories. This is precisely what agency (wakalah) is. The agent’s (wakil’s) task is to look after the interests of his principal (muwakkil). Certainly, Abdur-Rahman ibn Awf (radi Allahu anhu) must have done so after informing the Messenger of Allah (sallallahu alayhi wa sallam), upon which he did not object. From this, the validity of agency (wakalah) is established. Hafiz Ibn Hajar, quoting Imam Ibn al-Mundhir, writes that there is no difference of opinion regarding the permissibility of a Muslim appointing a harbi musta’man (a non-Muslim from the abode of war who seeks protection) as an agent, and likewise, a harbi musta’man appointing a Muslim as an agent. (Fath al-Bari: 4/605)
(2)
Why did Ibn Awf (radi Allahu anhu) make every possible effort to save a polytheist? The answer is that he took this step in view of the following objectives:
• One purpose in letting him escape was that he might be saved from death at that time.
• In the case of his escape, there was hope that he might embrace faith, perhaps he would become a Muslim in the future.
• By letting him escape, the aim was to break the prestige and grandeur of the disbelievers, because when his followers and supporters would learn that their leader had fled, they too would not remain on the battlefield. That is, the intention behind this action was to disperse their group and to protect the Muslims from their conspiracies.
(3)
Imam Bukhari (rahimahullah) has clarified at the end of the hadith that the meeting of Yusuf (alayhis salam) with Salih (alayhis salam), and of Ibrahim (alayhis salam) with his father, is established.
And Allah knows best.