When should he use the siwaak if he wants to do wudoo’?
Question

                I just want to ask you what is the ruling on jusing the Siwaak while doing Wudoo.

Is it better to use it after Wudoo ore before Wudoo.
Praise be to Allah.
      The scholars are agreed that it is mustahabb to use the 
      siwaak when doing wudoo’, because the Prophet (blessings and peace of 
      Allah be upon him) said: “Were it not that it would cause hardship for my 
      ummah, I would have instructed them to use the siwaak every time they do 
      wudoo’.”

    Narrated by al-Bukhaari in a mu‘allaq report. Also narrated 
    by Ibn Khuzaymah in his Saheeh (140) and classed as saheeh by 
    al-Albaani in Irwa’ al-Ghaleel, 1/109 

    It was also narrated by Ahmad (9612): “Were it not that it 
    would cause hardship for my ummah, I would have instructed them to use the 
    siwaak with every wudoo’.”

    Classed as saheeh by al-Albaani in Saheeh al-Jaami‘, 
    5317. 

    The scholars differed concerning the time for using the 
    siwaak when doing wudoo’. Some of them said that it should be before saying 
    Bismillah for doing wudoo’ and some of them said that it should be when 
    rinsing the mouth. 

    Ibn Nujaym (may Allah have mercy on him) said: 

    There was a difference of opinion concerning the time for 
    that. In al-Nihaayah and Fath al-Qadeer [which are books of 
    the Hanafi madhhab] it says that it should be when rinsing the mouth. In 
    al-Badaa’i‘ and al-Mujtaba it says that it should be before doing 
    wudoo. But most scholars are of the former view, which is more likely to be 
    correct, because it makes the mouth cleaner.

    End quote from al-Bahr al-Raa’iq, 1/21 

    Al-Zarkashi (may Allah have mercy on him) said: 

    The fact that it is mustahabb to use the siwaak is confirmed 
    in several places, at the time of prayer and when rinsing the mouth during 
    wudoo’.

    End quote from Sharh al-Zarkashi, 1/30 

    Al-Shirwaani (may Allah have mercy on him) said:

    The view of the author – meaning Ibn Hajar al-Haytami – is in 
    accordance with the majority, that it should be before saying Bismillah. And 
    the view we adopt is that it should be after washing the hands and before 
    rinsing the mouth.

    End quote from Hawaashi al-Shirwaani, 1/221 

    What seems to be the case is that the matter is broad in 
    scope, because there is no clear evidence from the Sunnah to stipulate any 
    particular time. 

    Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:

    Using the siwaak when doing wudoo’ should be with rinsing the 
    mouth, because this is the point at which the mouth is purified and the 
    siwaak is for purifying the mouth, as it is narrated in a saheeh report from 
    the Prophet (blessings and peace of Allah be upon him) that he said: “The 
    siwaak is purifying for the mouth and pleasing to the Lord.” So the siwaak 
    should come with rinsing the mouth, but if you wish you may use the siwaak 
    after finishing wudoo’ or if you wish you may use it before you start, but 
    it is better if it is done when rinsing the mouth.

    End quote from al-Sharh al-Mukhtasar ‘ala Buloogh 
    al-Maraam, 2/44 

    He also said:

    The scholars said that it should be used when rinsing the 
    mouth, because rinsing the mouth is purifying the mouth, so it should be 
    done at that point. But if that is not possible, then it may be done after 
    wudoo’. The matter is broad in scope. 

    End quote from Liqa’ al-Baab al-Maftooh, 133/31 

    The apparent meaning of the words of Shaykh al-Albaani (may 
    Allah have mercy on him) indicates that he thinks that the siwaak should be 
    used before saying Bismillah for wudoo’, as he said:

    The way it – wudoo’ – is done is: using the siwaak, saying 
    Bismillah, washing the hands three times – which is Sunnah – rinsing the 
    mouth, snuffing water into the nose and blowing it out.

    End quote from al-Thamar al-Mustataab, p. 9 

    And Allah knows best.