It's not clear from the quest log in your journal but you need to combine all the elements as a requisition.
Next time you hand in a requisition scroll through and you'll see the specializations will have their own req. You can then combine them and then go to the specialisation trainer.
The problem is that after taking the book, "Acquire writing on Reaver methods." part of the quest is not checked as completed.
Thus, as far as I'm aware, you can not progress with the quest, since it shows that you do not have the book, yet the book is removed from Iron Bull-s stuff and can not be purchased anywere else as far as I'm aware.
