Helmet purchases aren't something to be taken lightly. This is her life you are talking about. There is no other option than to have a helmet that fits properly. Believe me...if you, god forbid, should ever crash with her on it and she's injured b/c her helmet didn't fit properly...that would be absolutely terrible.
Take her to the shop...have her try on a every brand there. The helmet should be relatively tight...grab the chin bar when it's on her head and move it up and down and side to side. It should move...put pull her skin with it. Not excessively tight but not loose.
And finding a quality lid for under a benny is all but impossible. Look at the Scorpion lids. They are under 200 and very good quality.