Fanny is asked to play the role of Conscience by two different people.

First, Edmund comes to her for approval after he has decided to act the part of Anhalt himself. He knows he is on shaky ground here, and subconsciously wants Fanny to sooth over his qualms.

“Give me your approbation, then, Fanny. I am not comfortable without it.” Chap. 16

Next, Edmund wants Fanny to act as Henry's conscience, and guide Henry into a higher moral code.

"You will supply the rest; and a most fortunate man he is to attach himself to such a creature— to a woman who, firm as a rock in her own principles, has a gentleness of character so well adapted to recommend them. ... He will make you happy, Fanny; I know he will make you happy; but you will make him everything.”
“I would not engage in such a charge,” cried Fanny, in a shrinking accent; “in such an office of high responsibility!”
“As usual, believing yourself unequal to anything! fancying everything too much for you! Chap. 35

Finally, Henry himself wants Fanny to be his guide.

Would it not be worse than simple? Shall I go? Do you advise it?”
“I advise! You know very well what is right.”
“Yes. When you give me your opinion, I always know what is right. Your judgment is my rule of right.” Chap. 42

But Fanny's answer, and the right one, is this: “Oh, no! do not say so. We have all a better guide in ourselves, if we would attend to it, than any other person can be. Chap. 42