Can you help me with the wording in this note?

Only 4 of 9 girls in the class are included in the school directory (parental choice) but my daughter wants to invite them all. I can just explain the situation and go with it, but I would hate for anyone to feel excluded. Especially the new girl. Her teacher said I can write a note for her to give the students with my contact information so the parents can get in touch with me if they want to.

What I wrote is below, but I need to find a way to write it without using the student’s name because 1) there is a new girl in class with an unusual name I don’t know how to spell and 2) I can’t remember one of the girls and it is driving me crazy.

“Supacase Jr. would very much like to invite Emma to her birthday party! Since she has asked for a girls-only fairy party, I am unable to send invitations through school and I do not have any contact information for you. We would still love to include Emma if you are comfortable with that. Please contact me at 555–1234 or supacase@email.com and I will get an invitation to you.”

Or should I just say “screw it” and go with the four I have?