Have a search on here but I believe it's still Parcel Force, you're limited to £100 compensation, check this as it's off the top of my head and it's late ?
A claim involves relevant documentation - in the case of a sale the transaction qualifies as a receipt.
I have not claimed for a RIF but I have claimed for eBay and Vinted sales, Vinted wouldn’t be too applicable here as that usually includes Vinteds contracted carriers (and is passes over to Vinted to resolve in the ‘lost’ timeframe) but when Royal Mail is selected the seller deals with Royal Mail
I have managed to successfully claim value based on a screenshot of the transaction payment - of course up to the insured limit.
A private transaction should of course be paid via a suitable method (PayPal etc) and not tagged as friends & family money owed etc