Ted is the six-generation heritor of the know-how of papermaking. Does this sentense make any sense?

Yes. Personally, I would choose 'knowledge' instead of 'know-how', but it makes sense. I would also say 'from generation to generation', instead of 'through generation to generation'. If you want to use 'through', it would be a bit better to say it was 'passed through the generations'.

Somehow, I have the feeling that knowledge indicates the ability to write about paper making, while know - how implies an ability to do something. The distinction may be entirely in my own mind. Anyway, your sentence is good.

I'd wipe it.

Ted is a sixth generation papermaker.

That does sound good.

Thank U!