Child benefit for baby born in USA to EU mum.

Hi
One of my relative asked me this question she is EU Citizen and was living and working (treaty rights) in UK. She went on holidays to USA and gave birth to baby in US which she did not want. She paid a hefty bill for that now she returned to UK, she is asking if she can claim normal child benefit because she want to continue work, her child is american citizen by birth.
Also can she apply for Statutory Meternity Pay.

Thanks C001