It does not matter the injected bean is my own or seam's or weld's. They are all null. But no exception is thrown. The @PostConstruct never get called. But getAsObject and getAsString did get called.
If I inject those outside the converter, then they are not null.
Some people say it works for them: http://seamframework.org/Community/InjectionNotWorkingInFaceConverter?cid=2285991
But in my case, I have several seam 3 modules included in the war and I wonder if that makes injection in face converter not working? Seam faces developers, please help. I have tried everything I can think of.