If they're selling close to the original price, just get it from a shop instead, that way you'll get warranty etc too (there's generally no warranty on goods with "lost" invoices).
In general, look out for suspicious behaviour. Are they willing to meet with you at their home or office? Do they readily share their phone number? Do they have many excuses (one of the most common tells for liers are an excess of over-thought out excuses) for not doing things transparently? If it's too good to be true, it probably isn't true.
Sure, there are legitimate reasons for not getting any of these right, but if they get all of them wrong, be very careful.
Edit: never mind, just realized you're worried I or someone else is trying to sell stolen goods and will abuse such a list that way, sigh...
At any rate they didn't just say the information exists, they also said it was basic pawn shop training, so I googled "pawn shop detect stolen goods" the top answer was from quora https://www.quora.com/How-do-pawnbrokers-verify-that-the-ite... and there was something from a blog of somebody called the blog nerd which is a little difficult reading because of all the SEO keyword optimization he seems to have done
https://www.pawnnerd.com/how-do-pawn-shops-track-stolen-item...
there seemed to be a reasonable number of other informative links.
Interesting. In my area, Facebook Marketplace is almost all stolen/burgled/shoplifted goods. People even call it "Fencebook."
Want a brand new, unopened PS/4 for $25? Fencebook to the rescue!