First of all, this acne may be caused by scalp infection or inflammation. Because my mother once scratched when she felt itchy after dyeing her hair outside, it may have caused scalp injury during scratching, leading to infection or inflammation.
In order to determine the nature of this acne and get better treatment advice, I suggest my mother to see a doctor as soon as possible. Doctors can check this pimple to know its shape, color, size and other information, and some tests may be needed to determine its exact nature.
In addition, if mom doesn't want to see a doctor, she can try to apply some anti-infection or anti-inflammatory ointment to the acne, and pay attention to keeping the scalp clean and dry. If the situation does not improve or worsen, it is still recommended to seek medical advice as soon as possible.
I hope these suggestions are helpful to you. If you need more help or information, please feel free to consult a doctor or other professionals.