It's horrible, I agree. I personally would not tell the teachers about this though. First thing I would do is talk to her. Tell her what you think, tell her that you will not be missing any lessons because of her lie. Just warn her. If in the end people think you are unsympathetic, then so be it. At least you know the truth.
The thing is, her abusing the system will not affect people going through a genuine phase of depression (they will still receive the same help). In reality, this will only affect her (negatively), she is her biggest enemy right now. Just wait until she experiences real depression!
If the teachers find out about the recording or text message, it might not have very pleasant results for both of you. What if she then falls into real depression, because of this? She might not receive the help ever again. That would teach her something, but still these type of things might make her suicidal. (Okay, I know...lol..I am talking about worst case scenario)
What if she is just telling you that she is bluffing? Do you know for sure, that she is not going through depression or suffering in any way (at home etc).
From what I know, if you are applying for help from school/uni, you have to provide some kind of proof (medical). Maybe she is not comfortable telling you about her problems. If that's true, then it will only make you look bad. I would think a school would have made sure that it is not easy to fake an illness such as depression (and I am sure they are aware of this possibility). Otherwise, every second student would do that? Especially when missing homework, deadlines etc. Just what I think.
I would just leave her. All this receiving extra help might sound good, but if she is lying she will have to pay for it some way or another. Missing lessons, never helped anyone.