What should she do?

TBagpuss

I agree with tghe poster above that there is probably more to this - if she meets with HR  then I think she may do best to approach it as being unclear about why she's being told she won't be offered any further shifts - e.g. that she has not been told of any concerns about her performance, that the manager made the comment about her father but  that as she presumes that they would not stop offering her shifts just because a random person made malicious allegations about her she is trying to understand whether there are any concerns about her performance so they can be addressed.
If it's large enough to have HR her employer also probably has an employee handbook / manual - may be worth her looking up what their policies are around disciplinary matters etc - as if the reason being given if that she is dishonest then there is probably a process they should follow, but of course it may come down to her word against the managers or them simply taking the view that as there's no protected characteristic involved, the manager can stop offering shifts for any, or no, reason, and they won't get further involved. 

knightstyle

Thanks again for comments. basically HR said he denies it and as she has been there less than 2 years he can stop offering shifts at any time.
I think she will have to put this behind her, she is strong mentally as she has been through a lot and has already been offered another job.

Dakta

from the limited info here I'll answer the question from my perspective: -  remain positive and move on

Punishing the boss won't happen and would just add to the anguish