Once she is in the high register after doing slides, can she sing up there? Have you suggested that she tries to sing in a mock opera voice with any song?
She sounds husky in the recording, probably due to the cold! She is just literally not flipping over into the head voice at all which HAS to be isolated like it’s a separate person! This is what I do anyway. So only sing that high ending part on its own, getting her to open her throat like a yawn. “Ooo” vowel sounds are great for this. Hope it helps!