I would ask the person why she was interested in this specific religion and what she thought it could provide in the final days of her life. Although my first urge might be to tell her that she should rather adopt my own belief system, I do not believe that this would be the correct course of action. As a spiritual person, I believe in the right of everyone to choose his or her own path. I have no right to interfere with these choices, since they are so highly individualized. According to Kessler's various definitions of spirituality, it seems that each person and religious group adopts the system that is most comfortable and comforting to them.

The same would be the case for my dying friend. Not being in her shoes, I do not know exactly how she feels or what she needs. Just like in every other case, I have no right to tell my friend how or what to believe, or when to...

If she wants me to gather information about her new belief system, I will do so without questioning it. I will also bring any experts or advisers affiliated to the religion if she feels the need to consult with such people.
Dying is a unique and universal human experience. While we all die, each person experiences this differently. If my friend were to suddenly become spiritual after finding out that she was dying, I would therefore not question it, but indulge her in every possible way during the last months and days of her life. There is not reason to exacerbate the experience for her by engaging in useless religious arguments. Because it matters to her, I would help her to become as comfortable, both physically and spiritually, as possible.