There is no differing among the scholars, that I know of, over the permissibility of a Muslim giving a wasīyyah to his kāfir relative, since they do not inherit from him. And Ṣafīyyah ibnt Huyay gave a wasīyyah to her Jewish brother
From the Book of Allāh:
“After (the distribution of) a wasīyyah that was intended, or a debt” 
In this verse, Allāh lays down the legislation for how irth is to be distributed. Then, He legislates that the irth is to be distributed after any wasīyyahs or debts. In the next āyah as well, Allāh repeats this distinction three more times.
From the Sunnah of the Prophet (ṣallallāhu ʿalayhi wa-sallam): “Verily Allāh has given every person his true rights, so there can be no wasīyyah for a wārith (one who receives irth), and the child is for the (owner of the) bed, and the fornicator gets the stone (ie. nothing)…” 
Here the Messenger (ṣallallāhu ʿalayhi wa-sallam) forbids the one who receives irth from also receiving a wasīyyah. So obviously they are two separate things with different rulings.
What Exactly is a Wasīyyah Then?
Muḥammad ibn Aḥmad al-Ḥafīḍ (d.595), the author of Bidāyah al-Mujtaḥid, said: “The wasīyyah, in a nutshell, is a man giving a gift from his wealth to another or a group of people after his death, or that he frees his slave, whether he mentions the word ‘wasīyyah’ specifically or not.” 
So the wasīyyah is that which is given to someone according to the wishes of the deceased. It can be expressed verbally or in writing, and then it is witnessed. In the West, it is similar to when a man writes someone in his will to receive his house, car, or a sum of money.
We have been prohibited from taking the irth of the kuffār, according to the ḥadīth: “The Muslim may not take the irth of the kāfir, nor may the kāfir take the irth of the Muslim.” 
Does this prohibition also include the wasīyyah as well? Let us look to some of the statements of the scholars.
The Statements of the Scholars Concerning a Muslim’s Wasīyyah to a Kāfir
With regards to a Muslim giving a wasīyyah to a kāfir, then the scholars have unanimously agreed that it is permissible. Ibn ʿAbd al-Barr said: “There is no differing among the scholars, that I know of, over the permissibility of a Muslim giving a wasīyyah to his kāfir relative, since they do not inherit from him. And Safiyyah ibnt Huyay gave a wasīyyah to her Jewish brother.” 
Ibn Qudāmah al-Maqdisī (d.620) said: “The permissibility of a Muslim giving a wasīyyah to a Dhimmī has been reported from Shurayh, al-Shaʿbī, al-Thawrī, al-Shāfiʿī, Ishāq, and the Ḥanafīs. I do not know anyone who differed with them.” 
Al-Mārdīnī (d.912) said: “It (the wasīyyah) is allowed to be given to the poor people of a specific area, or a band of them, and to a Dhimmī, a young child, or an insane person by agreement of the scholars.” 
The statements of the scholars concerning the kāfir’s wasīyyah to a Muslim
The scholars have also agreed that a Muslim may accept the wasīyyah of a kāfir. Ibn al-Munthir (d.318) said, relating a consensus: “All of the people of knowledge that we take from have agreed that the wasīyyah of a Dhimmī (a Jew or a Christian living under Islamic rule) is permissible, so long as the thing given itself is permissible to possess.” 
Muḥammad ibn Aḥmad al-Ḥafīḍ (d.595), the author of Bidāyah al-Mujtaḥid, said: “And the wasīyyah of a kāfir is permissible to take according to them (the imāms), so long as the wasīyyah is not something ḥarām in itself.” 
Ibn Qudāmah Al-Maqdasee said: “So when it is permissible for a Muslim to give a wasīyyah to a Dhimmī, then a Dhimmī’s wasīyyah to a Muslim, or to another Dhimmī, has even more right.” 
Muḥammad ibn Ṣāliḥ al-‘Uthaymīn (d.1421) said: “If someone asks, ‘How can one’s parents not be considered wāriths?’ The answer: That is possible, like when the mother or father has a different religion, then they do not take any irth, rather they can be given a wasīyyah.” 
If one of Fulān the Muslim’s kāfir relatives dies, and he/she left for Fulān a sum of money or some kind of property or wealth, having specified it for Fulān, either in writing or by speech or gesture, and, as a result, that wealth is then offered to Fulān, then it is permissible for Fulān to accept it, and it is from Allāh’s ḥalāl provisions for him. And Allāh is Al-Muwaffiq.
The next question that we need to have answered in this thread is:
What if the kāfir relative specifies Fulān to receive more than one-third of his/her wealth? The Prophet (ṣallallāhu ʿalayhi wa-sallam) forbade us from giving someone more than one-third of our wealth as a wasīyyah. The scholars have two positions with regards to the one who left a wasīyyah of more than one-third:
1) Only up to one-third may be given, and the rest is to be distributed as irth.
2) The entire wasīyyah can be given only with the consent of all the inheritors. If they do not agree, then only up to one-third is given and the rest is distributed to the inheritors.
So then does this apply to the kāfirs? Do we restrict them to one-third as well? If Fulān’s kāfir relative leaves everything as a wasīyyah for him, can he take it? May Allāh assist us in finding answers from the people of knowledge for these important questions!