When you're at the stage of trying to get the book to Joe, DO NOT "solve" the fridge puzzle before the book is on the way. I did that wrong and automatically switched to Joe without the possibility to get the book or switch back to Christine.
After brute-forcing - i. e. in every room use every item with every action point, transitional point and other inventory item - failed I resolved to check a walkthrough and found out I was supposed to get the book from the Chaplain who still points to Christine who is unavailable.