The US didn't just convince them to, the US was a big part of the development of technology with a government/industry consortium in the late 90s (EUV LLC) with

The US didn't just convince them to, the US was a big part of the development of technology with a government/industry consortium in the late 90s (EUV LLC) with DARPA being a big part. That partnership worked with ASML under terms that are now letting the US have a big say in export controls.