Pensioner savings question

Hi,

I am here on behalf of my parents. We can't get to the bottom of a situation and I hope someone can help.

Situation
OK, so Father is 71, Mother is 64 (65 next Feb)
They recently spilt up. Mother has gone into private rented accomodation, Father still in marital home (up for sale).

Mum now gets housing benefit (about 2/3 cost of rent) and pension guarantee (£21 plus state pension and will get an extra £5 pension savings credit when she is 65 next year).

Father also gets pension guarantee and pension savings credit.

I don't think either of them pay council tax at the moment.

When the house sells, my Father will move into private rented accomodation. I think they will have about £40k cash each. No private pensions.

Question
When the house is sold and my Father moves into rented accomodation, what will they be able to get in help housing benefit and council tax? We thought nothing, but then I read if they are on pension guarantee the savings will be disregarded and they can get housing benefit and council tax benefit?

Is that correct?

Thanks,

Pb