Thanks for your question.
I assume that you are permitted to claim housing benefit and that you are not yourself here in the UK on a visa which does not permit this. If you are on a visa and are not allowed to claim public funds under the terms of that visa then you should not disclose to the UKBA because that could lead to your visas being terminated.
My reference to public funds in my earlier question was with regard to your mother. She is not permitted to claim public funds and must show by the money she has available (and your offer of sponsorship) that she will not need to claim any additional monies.
The housing benefit would be a problem to your mother's application, if she has the money to fund her visit she will still be fine even though you are claim housing benefit. However, a person's offer to sponsor another person is only as good as the money held in the sponsor's account so you will have to show that you have funds to cover the costs of any unforeseen expenses of your mother's stay here. If you can do this she will be fine.
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