Running the Fingers through the Beard in Wudu
Question

What is the ruling on running the fingers through the beard when doing Wudu? What is the most correct scholarly view?
Praise be to Allah.Ruling on running the fingers through the beard in Wudu
If the beard is light and the skin of the face beneath the beard can be seen, then it is obligatory to run one’s fingers through it and wash what is beneath it, because it is included in the definition of the face [which must be washed in Wudu].
But if the beard is thick and the skin of the face beneath it cannot be seen, then it is not obligatory to wash what is beneath it, but it is recommended to run the fingers through it according to the majority of scholars, and this is the most correct view.
Ibn Qudamah (may Allah have mercy on him) said: 
“If the beard is light and shows the skin, then it is obligatory to wash what is underneath it. But if it is thick, it is not obligatory to wash what is beneath it, but it is recommended to run one’s fingers through it.
Ishaq (may Allah have mercy on him) said: If the man deliberately omits to run his fingers through his beard, he must repeat [Wudu ], because the Prophet (blessings and peace of Allah be upon him) used to run his fingers through his beard. This was narrated from him by `Uthman ibn `Affan. At-Tirmidhi said: This is an authentic Hadith. Al-Bukhari (may Allah have mercy on him) said: This is the soundest Hadith concerning this matter. Abu Dawud (may Allah have mercy on him) narrated from Anas (may Allah be pleased with him) that when the Prophet (blessings and peace of Allah be upon him) did Wudu, he took a handful of water and made it reach under his chin, and he said: “This is what my Lord, may He be Glorified and Exalted, instructed me to do.” It was narrated that Ibn `Umar (may Allah be pleased with him) said: When the Messenger of Allah (blessings and peace of Allah be upon him) did Wudu, he would rub the sides of his face then run his fingers through his beard from underneath. (Narrated by Ibn Majah)
`Ata’ and Abu Thawr (may Allah have mercy on them) said: It is obligatory to wash the underside of facial hair, even if it is thick, as is required when doing Ghusl for Janabah , because it is enjoined to wash the face when doing Wudu just as it is enjoined to wash it when doing Ghusl for Janabah ; what is obligatory in one of them is also obligatory in the other.
The view of most of the scholars is that it is not obligatory, and it is not obligatory to run the fingers through the beard. 
Among those who granted a concession allowing the man not to run his fingers through his beard were Ibn `Umar (may Allah be pleased with him),and Al-Hasan ibn `Ali, Tawus, An-Nakha`i, Ash-Sha`bi, Abu Al-`Aliyah, Mujahid, Abu Al-Qasim, Muhammad ibn `Ali, Sa`id ibn `Abd Al-`Aziz and Ibn Al-Mundhir (may Allah have mercy on them). That is because Allah, may He be Exalted, enjoined washing, but He did not mention running the fingers through the beard, and most of the reports which describe the Wudu of the Messenger of Allah (blessings and peace of Allah be upon him) do not mention it. 
If it was obligatory, he (blessings and peace of Allah be upon him) would have run his fingers through his beard when doing Wudu, and if he had done that every time he did Wudu, all or most of those who narrated reports about his Wudu would have mentioned it. 
The fact that he (blessings and peace of Allah be upon him) did not do it indicates that washing what is beneath the thick hair [of the beard] is not obligatory, because the Prophet (blessings and peace of Allah be upon him) had a thick beard, so the water would not have reached what was beneath it without running the fingers through the beard and doing that thoroughly. The fact that he ran his fingers through his beard sometimes indicates that doing it is recommended [but not obligatory]. And Allah knows best." (Al-Mughni, 1/74)
An-Nawawi (may Allah have mercy on him) said: 
“With regard to a thick beard, its surface must be washed, with no difference of scholarly opinion, but it is not obligatory to wash it deeply or to wash the skin underneath it. This is the well-known correct view which was stated by Ash-Shafa`i (may Allah have mercy on him) and was stated definitively by the majority of his companions. It is also the view of Malik, Abu Hanifah, Ahmad (may Allah have mercy on them) and the majority of scholars among the Companions, the Followers and others.
Ar-Rafa`i (may Allah have mercy on him) narrated a different view, which is that it is obligatory to wash the skin [beneath the beard]. This is the view of Al-Muzani and Abu Thawr (may Allah have mercy on them)." (Al-Majmu`,  1/408).
Evidence against mandating running the fingers through a thick beard
Among the evidence quoted by the majority of scholars to prove that running the fingers through a thick beard is not obligatory, and that the inside of the thick beard does not have to be washed, is the report narrated by Al-Bukhari (140) (may Allah have mercy on him) from Ibn `Abbas (may Allah be pleased with him), which says that he did Wudu and washed his face. He took a handful of water and rinsed his mouth and washed his nose with it. Then he took another handful (of water) and did like this, putting his hands together, and washed his face with them … Then he said: This is how I saw the Messenger of Allah (blessings and peace of Allah be upon him) doing Wudu.
The evidence in this Hadith is the fact that the Prophet (blessings and peace of Allah be upon him) had a thick beard, and one handful of water is not sufficient to wash both the face and what is under the beard. Thus it is known that he (blessings and peace of Allah be upon him) washed the surface of the beard only. (See: Al-Majmu`, 1/408, and Nayl Al-Awtar, 1/190)
Evidence of the view that mandats running the fingers through the beard
Those who regard it as obligatory to run the fingers through the beard quote as evidence what was narrated by Abu Dawud (145) (may Allah have mercy on him) from Anas ibn Malik (may Allah be pleased with him), that when the Messenger of Allah (blessings and peace of Allah be upon him) did Wudu, he took a handful of water and made it reach under his chin, by running his fingers through his beard, and he said: “This is what my Lord, may He be Glorified and Exalted, instructed me to do.”
There is a difference of opinion regarding this Hadith. Al-Hafiz Ibn Hajar (may Allah have mercy on him) said: Regarding the Hadith of Anas, it was narrated by Abu Dawud, and its Isnad (chain of narrators) includes Al-Walid ibn Zarwan, whose status is unknown.
It has other Isnads from Anas (may Allah be pleased with him) which are inauthentic." (At-Talkhis al-Habir, 1/86)
However, the Hadith was classed as authentic by Ibn Al-Qayyim (may Allah have mercy on him) in Tahdhib As-Sunan and by Al-Albani (may Allah have mercy on him) in Sahih Abu Dawud.
Assuming that the Hadith is authentic, the instruction in it may be understood to mean that this action is recommended, so as to reconcile between this Hadith and other evidence, because most of the reports which speak of the Prophet’s Wudu do not mention running the fingers through the beard. If it was obligatory, he would have run his fingers through his beard when doing Wudu , and if he had done that every time he did Wudu, all or most of those who narrated reports about his Wudu would have mentioned it.
Washing the surface of a thick beard
It should be noted that the surface of a thick beard must be washed, even if it is long, because it is included in the definition of the face; therefore it is obligatory to wash its surface.
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: 
“One of the recommended acts of Wudu is running the fingers through a thick beard, because a beard is either light or thick.
The light beard is that which does not cover the skin; in this case the beard and what lies beneath it must be washed, because if what lies beneath it is visible, then it is part of the face, which is what is seen when one person faces another. The thick beard is that which does cover the skin; in this case it is only required to wash its surface. According to the well-known view in our (Hanbali) Madhhab, it is obligatory to wash a long beard down to its end.
However, it was also said that it is not obligatory, just as it is not obligatory to wipe over long hair that goes further than the neck. Yet, the view that is most likely to be correct regarding this, is that the beard must be washed, and we should differentiate between the beard and the hair, because even if the beard is long, it  is included in the definition of the face, whereas long hair is not included in the definition of the head."(Ash-Sharh al-Mumti`  1/106)
And Allah knows best.