My children have all studied music theory with a private tutor. She used the Music Theory in Practice Grade 1-5 by Eric Taylor and also Theory of Music Workbook by Harold Jones Grade 1-5 (these are out of print I think she used copies). Text books she used The AB guide to Music Theory part 1 by Eric Taylor and A Handbook of Musical Knowledge by Murray Brown. My children in addition also studied a thorough program of rhythm reading which was so helpful.
Admittedly the text books are NOT for children. Your friend would have to study the subject and be able to convey it to your child.
Let me know if you want to contact this teacher to get more advice on good study materials.