Best way to do a "double closing"?

I have a CASH buyer who wants me to find her a DW park home. What is the best way to do the deal so she can buy it right after I close on it. I would rather she didn’t know what I paid for it. The home I am looking at is listed w/a local agent and I was thinking I would just use her cash to pay so I don’t have to hassle with my HELOC. What is the best way to make this happen?