How to accept an unsolicited offer while auction is running

I'm selling a phone via an auction on eBay Australia. It's currently at about $250 with 6 days to go. There's no "Make an Offer" or "Buy it Now" buttons on my listing. Nevertheless, I've received an unsolicited and acceptable much higher offer via a direct message. The buyer has 100% feedback as a buyer and has been a member for 10 years, so he seems legit.

But (as I've never accepted an offer during auction before) I'm not sure how to do this and keep eBay happy. The only way I can think of to do this, would be to kill the auction and re-list with a fixed price and tell the guy to go for it.

Is that how it's done?

NB: I've read that in some countries, or at least the US of A, there are "Make Offer" and "Decline/Accept/Make counter-offer" buttons in direct messages, but I've never seen those in my Aussie messages.

Steve