Samuel Slater apprenticed at a British cloth factory and memorized the design. Then he emigrated to the US and set up shop. Although, I think it might be more correct to say that the US allowed him to steal IP, rather than the country stealing it.

https://en.wikipedia.org/wiki/Samuel_Slater

I think that US publishers, especially sheet music publishers, would copy British music and and publish it in the US, since I don't think that the US honored British copyright (at least some subset of it), but I can't think of good search terms to find any sources.