Is it permissible to continue memorizing the Qur’an and receiving lessons in religious knowledge online if one of the female teachers has her fifteen-year-old son sitting with her?

Utilizing modern communication tools for memorizing the Quran is a good thing, and one should persevere in it and not pay attention to the whispers of Satan. The voice of a woman is not considered awrah (private/exposeable), but her recitation of the Quran with melodious intonation and softening of the voice might cause fitnah (temptation/discord). Therefore, she should conceal her recitation from non-mahram (definition) men.