How do I report someone who holds a Green Card but commits fraud by not living in the US, further using an address in the US to collect child support, although children are not living in US?

Green card holders who live overseas permanently lose their status automatically if they are outside US for over 12 months without having a re-entry permit.

Legal status and child support are different issues and should not be combined. If the child lives overseas and the parent who pays child support lives in US, it's not fraud...