Is it permissible for my mother—who does not memorize the verses of the Qur’an nor is she able to do so—to pray with only the movements without reciting Al-Fatihah or the short surahs?

If a mother is unable to learn Al-Fatiha, the prayer does not fall away from her. Rather, she must pray in the manner mentioned in Fatwa no. 9942. Ibn Arafa said: "Whoever is ignorant of it must learn it. If time is short, he should pray behind an imam. If he cannot find one, then according to Ibn Sahnoun, Ibn Al-Qasim, and Ashhab, his obligation is to remember Allah," meaning he says the opening takbeer (takbeerat al-ihram), remembers Allah, and then bows.