There is nothing wrong with implanting an artificial tooth with a ceramic crown in place of a broken tooth, whether the implant is permanent or temporary.
There is also nothing wrong with leaving it in place after a person dies; there are no shar’i reservations about burying a person with an artificial tooth.
The artificial tooth does not have to be removed during wudoo’ or ghusl, as some people think, because it is sufficient to rinse out the mouth.
The scholars of the Standing Committee for Issuing Fatwas were asked: Is removing the teeth and replacing them with new teeth regarded as changing the creation of Allaah?
There is nothing wrong with treating damaged or faulty teeth with something which will remove the harm they cause, or extracting them and replacing them with false teeth, if there is a need for that, because this comes under the heading of permissible treatment to remove something harmful; it does not come under the heading of changing the creation of Allaah as the questioner understands it, because what is meant by the fitrah in the verse “Allaah’s Fitrah (i.e. Allaah’s Islamic Monotheism) with which He has created mankind. No change let there be in Khalq‑illaah (i.e. the religion of Allaah __ Islamic Monotheism)” [al-Room 30:30] is the religion of Islam. End quote.
Fataawa al-Lajnah al-Daa’imah (25/15).
It also says (25/57):
There is nothing wrong with having your teeth treated by a dentist who specializes in dealing with deformities and changing faults by adding artificial teeth, because the Prophet (peace and blessings of Allaah be upon him) said: “Yes, O slaves of Allaah, seek medical treatment, for Allaah has not created any disease but He has also created it cures – or its medicine – except one disease.” They said: O Messenger of Allaah, what is it? He said: “Old age.” Abu ‘Eesa (al-Tirmidhi) said: Similar reports were narrated from Ibn Mas’ood, Abu Hurayrah, Abu Khuzaamah from his father, and Ibn ‘Abbaas. This is a hasan saheeh hadeeth.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: Is it permissible to use false teeth in the mouth when the natural teeth fall out and there is a need for that?
He replied: It is permissible, if a person’s teeth fall out, to replace them with false teeth, because that is removing a fault. The Messenger (peace and blessings of Allaah be upon him) gave permission to one of the Sahaabah (may Allaah be pleased with him) whose nose had been cut off to use a nose made of silver, but it began to smell bad, so he gave him permission to use a nose made of gold, so he used a nose made of gold. Similarly, if the teeth fall out, then one may use false teeth instead, and there is nothing wrong with that. End quote from Fataawa Noor ‘ala al-Darb.
To sum up, there is nothing wrong with your mother having an artificial tooth permanently implanted.
And Allaah knows best.