He traced it back to the Prophet ﷺ, who said, "Were it not that I would impose hardship on the believers, I would have ordered them to delay the night prayer and to use the siwak before every prayer."
حدثنا قتيبة بن سعيد عن سفيان عن أبي الزناد عن الأعرج
يرفعه قال لولا أن أشق على المؤمنين لأمرتهم بتأخير العشاء وبالسواك عند كل صلاة
Reported by Muslim, in the Book of Purification, Chapter on the Tooth-stick, hadith no. 252, from Qutayba, and by Bukhari, in the Book of Friday Prayer, chapter, hadith no. 887, 7240, from the hadith of Abu Zinad with the same wording. It was also narrated by Nasai, hadith no. 7, Friday chapter, hadith no. 887, concerning the day for using the tooth-stick, and by Ibn Majah, hadith no. 287.