Hello, I'm writing to you with some sources regarding cremation. The issue is complex...
In principle, in the Torah (Devarim 21:23): “you shall bury him”, it clearly says that the dead body must be buried.
The Talmud (Sanhedrin 46b) discusses whether burial is intended to avoid showing contempt for the body or for atonement. The difference lies in who is arguing against burial: if the burial is intended to avoid showing contempt, we won't listen, whereas if the burial is for atonement, if the person isn't interested in atoning for their sins, then we don't bury them! The Talmud doesn't reach a conclusion...
Maimonides (Laws of Mourning, Chapter 12, Halakha 1) writes, based on this Talmudic discussion: “If he commands that he not be buried, we do not listen to him, since burial is a biblical precept, as it is written, 'You shall bury him.'” In the commentary Kesef Mishnah (in the same passage), he quotes the opinion of Ramban (Nachmanides): ”Therefore we bury him, because it is a biblical matter. Even if the heirs do not want to bury him, we take him (from the dead) by force. And even if a dead person has no one to bury him and says not to be buried, we do not listen to him, since it is a disrespect shown by all the living (that is, all of us who do not attend to his burial are showing disrespect to the dead person), and not only by the family.“.
This is expressed in the Shulchan Aruch, Yoreh De'ah, 362:1: "The best thing is to bury in the earth literally, even outside of Eretz Israel.".
In other words, from all these sources, it is clear that burying the dead in the earth is a mitzvah (as stated in Nitei Gavriel, chapter 75:1). Therefore, holes are also made in the coffin before burial, so that it has literal contact with the earth.
Now, if the person orders cremation, a responsa (Jatam Sofer, Iore Dea 341) suggests that in the last moment before dying, the person may have regretted the cremation, since even a simple thought of regret is sufficient (at least in that situation). Given this, who's to say they won't regret what they're ordering? Even if it's just a doubt that they regret it (and the Jatam Sofer writes, "they almost certainly regret it"), once cremated, there's no going back...
Yes, God forbid, she was cremated. Apparently, according to rabbinic responsa, the ashes must be buried in a Jewish cemetery, but separated from other people, at least 4 meters away. However, this is something to check, because generally they are not buried, there is no mourning for the person, no Kaddish is recited, as if nothing had happened, because it is considered that they have completely abandoned Judaism...
From a spiritual perspective, burial is part of the expiation process, both for the body and the soul. If a person is not buried, this expiation is lacking. Therefore, even if there were a question of halakhic law (whether it's to avoid showing contempt for the body or for the sake of expiation), when in doubt, it's best not to risk a person's expiation by cremating them.
I am transcribing some parts of the book Maavar Iabok, Sfat Emet, a book that speaks especially about death from a mystical perspective.
In chapter 26 it says: “The soul recognizes the honor of the body, and its contempt after death. With this we will understand and know that kindness to the body means kindness to the soul […] and no dead person should be disrespected.”.
In chapter 27 he writes: “The secret of burial is a satisfaction for the soul. As long as the body does not lie in its place, the soul is not at peace […] As long as the body is not buried, the soul does not rise at all […] that is why we bury the body, earth below […] earth above […] with this we make the soul rise very high with the concept of burial and the action.”.
Another aspect of the issue is that it is one of the Thirteen Principles of Faith in Judaism, as written by Maimonides: the Resurrection of the Dead. If a person is cremated, they are essentially denying that God will resurrect the body. The Mishnah in Sanhedrin 10:1 clearly states that while all the Jewish people have a share in the World to Come (i.e., in the Resurrection of the Dead), it also clarifies that those who deny it will not participate in it.
In short, it is clearly forbidden to cremate a Jewish body, even if the person requests and orders to be cremated; we do not comply, it is part of our faith and beliefs in the eternity of the soul and body at the moment of the Resurrection.