I typically suffer from migraines, but after having found what triggers them I am able to manage them much more effectively as a general rule. For me I am influenced by caffeine, preservatives in foods and dehydration.. I have really cut back on the tea and coffee, but found during phase 1 that I was REALLY thirsty and felt quite dehydrated everymorning. To help combat that I drank three litres of water each day on phase 1. I also eat mostly organic fruit, vege and meat and steer away from prepackaged foods as much as possible.
As Ellis mentioned sugar detox can be pretty tough on the body, but I found once the first 3-4 days was done the improvements were immense.
Perhaps if your friend is experiencing the migraines past the first 4 days she should switch to phase 2 and monitor how she is feeling. Perhaps the SBD is unrelated to her migraines if it continues.
I hope she is feeling beter soon... and good vibes for your new healthy eating for the two of you. Just as a side bar.. if your friend hasn't found what triggrs her migraines I have a webpage that can assist with elimination diets to isolate food related problems if you would like it for her.. it is based here in Australia but the information should be relevant worldwide. Just PM me if you would like it.