Couples question

Hello - I am not sure if a question I asked a couple of days ago 'glitched' and disappeared due to my non-tekkie skills so am writing again for some help.

I have found myself in a situation by chance that seems awkward and need to seek clarity.
Some months back I had to move out of my rental place and I found a rental annexe to go to. There was a 'gap' between moving out and moving in so my Ex-husband said I could stay over at his place temporarily. I thus went ahead with my arrangements, put my stuff in storage etc and moved in to his spare bedroom. We are friends but not a couple. He is over 70, lives in sheltered housing, receives Pension credit and HB. I am in the Support Grp of ESA. I have some savings so I just get the part that is allowed when you are means-tested.
Fast forward some weeks/a month or so and I am told the annexe has fallen thro. I have nowhere to go and rentals round here are extremely difficult to find. Ex says I can stay with him until I find somewhere and we inform the DWP and HB of the situation.
HB have now written to him to ask him if I am still staying with him. My worry is that HB may try to make out we are a couple and then take away his HB/Pension credit/CT discount saying that I can pay for everything as I have savings. We are not a couple. We sleep in separate rooms, have separate cars and bank balances and have clearly not been living together since we divorced back in 2008. We have both had other partners altho right now we are both single. So I am a bit worried as to what to say to them as I understand they may use trick questions to try and make out we are a couple when we aren't. I am temporarily lodging with him, which his tenancy agreement allows. Pls can you advise? Thankyou and sorry if you DId get my previous query on this and it is just in a queue.