All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
Most of the scholars are of the view that using the Siwaak is a confirmed act of the Sunnah. It should be used at all times, particularly on five occasions: before one prays, performs Wudhoo’ (ablution), recites the Quran, wakes up as well as when the mouth smells bad. As evidence, ‘Aa’ishah narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "(Using) the Siwaak purifies the mouth and pleases The Lord." [Ahmad and An-Nasaa‘i]
There is no doubt that this ruling includes those who have either natural or false teeth. That is because the purpose of using the Siwaak is to keep the mouth clean and free of any offensive odur. Given that, false and natural teeth are the same in this respect.