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Hi - I've just done exactly that - reiterated facts (royal mail shows delivered and received by a person giving your surname), added tracking to the opened case and tracking transcript, very polite, and said "I'll follow up with Royal Mail and eBay this morning and forward and relevant information immediately, as received." Within 5 minutes of sending it, the case was closed.
I can't see a legitimate scenario where a buyer opens a case for non-receipt at 2315 on Thursday then closes it, with no explanation/msg, at 0815 the following day
odd all round - hopefully the last I've heard of this.
I'd be providing all the information you can to prove the delivery. Sounds like you have that from the royal mail. Share everything you have now, and advise your next steps that you're following up with additional info from the royal mail
If the item has been delivered and signed for as it says, I feel like the buyer needs to prove that's the not the case somehow.
They've opened a case, so just deal with it in a friendly manner through that process.