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How hard did the family actually try to solve this mystery though?

To be fair, this wasn't searchable in 1996. :)

They rediscovered the card a couple days ago and the string of characters only results in the content itself. https://www.google.co.uk/search?q=OFWAIHHBTNTKCTWBDOEAIIIHFU...

The solution was someone recognizing the pattern, not arbitrary Googling, which I find far more interesting.

Actually, arbitrary Googling works pretty well. Just start chopping letters of the end, and you get a hit on "OFWAIHHBTNTKCTWBDOEAIIIH" from 2007.