Housing Benefit proof of single payment.

I am British with 2 British Children and Wife on Spouse Visa.
I applied for Housing benefit last month, I wrote in the form that please do not include my wife as she is not allowed to take public funds. I kept the photocopy of that page.
Secondly, when I met with the council staff I asked him again and he said he is aware about my wife immigration status. I had provided them copies of my wife's BRP and passport.

Now I have received the calculation page of the benefit approval but it didn't say that only one parent is included in the benefit.
I want to know that how can I prove to Home office in future that my wife did not take any benefit. Will I have to mention in the FLRM form that I am getting housing benefit but my wife is not getting any benefit. what proof I will have to keep with me for our future application.

Many Thanks