Here's a link to the history of Stand Up Paddle Boarding on the Surfing side of things. It was a long time ago!!
http://www.supglobal.com/stand-up-paddle/stand-up-paddle-surfing-articles/6-the-history-of-stand-up-paddle-surfing.html
If you're interested in how we started doing it up here on Lake Tahoe, a few core locals have been paddling on longboards during the summer months for quite some time (most likely since the early '70s) after the Olympics brought us up to standard with other destinations.
As for full-on lake born, stand up paddleboard touring? Us and a few others started up about six years ago. Three years ago our founder Nate Brouwer decided to head out on the lake for a paddle on a typical board. It didn't work! It needed a displacement hull, so he back to the drawing board and started making his own boards.
Here's our story -
http://tahoesup.com/#/about
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It is not entirely clear, but I have seen it suggested that Graeme Fuller's idea for a cheap, fun easy, Mal style board ulimately led to the creation of the stand-up paddleboard, so it could be argued that Graeme Fuller (sometimes fondly known as 'Grumpf')was the inventor of the SUP.