Both her partner AND Student Funding could press charges against her forging their signatures.
However,at the present time I would advise her to sit tight and wait and see what happens.There is no point in rushing into admissions of guilt if nobody thinks that you have done something to be guilty of.
It strikes me that the person she will have to apologise to and try and placate is the partner,if her forgery results in him not gettting his funding.
So,in short:~
Don't write to Student Funding,I think they already know what is going on,wait and see what they say.
No, don't go to the police,I don't think they would be interested anyway,and they would probably regard it as a civil not criminal matter.
Sit tight and see how things pan out,and deal with them as they happen.She cannot take back what she has done,she can only hope it all blows over,so to speak.
I amsure things will not be as bad as she thinks,it all may seem black at the moment,but all things pass.