The siwaak (tooth-stick) :
The siwaak is recommended in all conditions, and its recommendation is emphasized:
1- Along with the wudoo·:
From Aboo Hurayrah -radiyallaahu `anhu- who said: Allaah’s Messenger (صلّى الله عليه وسلّم ) said:
<<If it were not that I would make a difficulty upon my nation I would have commanded them to use the siwaak with every wudoo·.>>” 
2- At every Prayer:
From Aboo Hurayrah -radiyallaahu `anhu- from the Prophet ( صلّى الله عليه وسلّم ) who said:
<<If it were not that I would make a difficulty for my nation I would have commanded them to use the siwaak at every Prayer.>> 
3- When reciting the Qur·aan:
From `Alee -radiyallaahu `anhu- who said: “He commanded us to use the siwaak, and he said:
<<When the servant stands in Prayer an Angel comes to him and stands behind him, listening to the Qur.aan and drawing closer. So he continues listening and drawing closer until he places his mouth upon his mouth. So he does not recite any Aayah except that it enters within the Angel>> 
4- When entering the house:
From al-Miqdaam ibn Shurayh: from his father, who said: I asked `Aa·ishah, saying: “What had the Prophet ( صلّى الله عليه وسلّم ) used to begin with when he entered his house?” she said: “With the siwaak.” 
5- When getting up (to pray) during the night:
From Hudhayfah –radiyallaahu `anhu- who said: “When Allaah’s Messenger ( صلّى الله عليه وسلّم ) got up to pray the tahajjud Prayer at night, he used to rub his mouth with the siwaak.” 
 Saheeh: Saheehul-Jaami` (5317); Ahmad (1/294/171).
 Agreed upon Muslim (1/220/252), al-Bukhaaree (2/374/887), at-Tirmidhee (1/18/22), an-Nasaa·ee (1/12); except that the wording of al-Bukhaaree is: “with every Prayer.”
 Saheeh Lighairihi: as-Saheehah (1213); al-Bayhaqee (1/38).
 Saheeh Ibn Maajah (235); Muslim (1/220/253) Aboo Daawood (1/86/58), Ibn Maajah (1/106/290), an-Nasaa·ee (1/13).
 Agreed upon: Muslim (1/220/255), and this wording is his; al-Bukhaaree (1/356/245), Aboo Daawood (1/83/54), an-Nasaa·ee (1/8); and the wording of the three is: “When he got up (to pray) during the night.”
Source : Al-Wajeez, The Book Of Purification – Abdul-`Azeem ibn Badawee al-Khalafee, Translated by Abu Talhah Dawood Burbank .
Related Link: https://abdurrahman.org/tahara-purification/