Longest trading stocks, NYSE and London

From here I noticed that the longest listed company on the NYSE is Con Edison, though of course they’ve changed a bit since their arrival way back in 1824. Suppose that a handful of New York Gas Light Company share certificates were discovered, stuffed away in an attic trunk for all that time. Could they be redeemed today as Con Edison shares?

In general, do stock shares come with an expiration date, or other conditions of invalidation? And has anyone ever sold shares that were over a century old?

I’m also curious what the longest listed company on the London Stock Exchange is, but Googling has so far failed to churn it up. Anyone know?