Is praying for a female teacher who has no children considered an ongoing charity (sadaqah jariyah) for her, and does this fall under the meaning of the hadith: "or a righteous child who supplicates for him"?

It is permissible to supplicate for the teacher, and the supplication will benefit them, reaching them as a reward. This is a form of recompense for kindness and a return of good. As for ongoing charity (sadaqah (definition) jariyah), it refers to an endowment (waqf), such as building a mosque or digging a well. This supplication is neither part of it nor what is intended by "child" in the hadith (definition).