Housing benefit - partner on limited leave to remain

[Eaustin]

I would like to ask a question for a friend.

He has PR
His partner has just received a visa - limited leave to remain until April 2015 as parent of a child born in the UK (she had overstayed her original visa).
They have a 4 year old child born here.
They all live together in a one-bedroom flat.

Is my friend entitled to apply for housing benefit? If so how should his partner be declared on the form? i.e. should she be included or excluded

If further information is required please let me know.

Thanks in advance.

[Amber]

On the partner's BRP does it say no recourse to public funds? Which Country is the partner native?