No, Shomer, you don't understand. She was not made redundant and did not resign - she was dismissed on grounds of capability. And there will be nothing specifically in the employment contract about this - I'll guarantee it.
I agree with Zacmaster. If this is the wording of the letter was this, she is entitled to 4 weeks pay per year of completed service, and one suspects they have messed-up. 4 weeks is not unheard of, but is rather generous.
However a contract is a contract, and they will have to honour it. I suspect you are going to have to engage a solicitor unless you are happy to start writing letters threatening legal action.