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That's a shame.  It doesn't hurt the father, as long as he is not filing a US tax return.  So while it is fraud, and is reportable, it also seems somewhat spiteful.

Anyway, for one set of dependent rules, the child must live with the parent for more than half the nights of the year, or get a signed release form from the other parent.  And for the other set of rules, it doesn't matter where the child lives but the taxpayer must provide more than half the child's support.

It's all in here <a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p501.pdf">https://www.irs.gov/pub/irs-pdf/p501.pdf</a>

Penalties for underpaying tax are about 1% per month of the amount underpaid, figuring each year separately.  Plus a potential of an additional 25% penalty for deliberate fraud.  If the IRS views this as deliberate, the statute of limitations is 6 years from the date the return is filed, or the April 15 deadline, whichever is later.  So at this point, she could be audited for the 2012-2017 returns, assuming they were filed on time.  

The dependent and child tax credit for 2012 could have been worth about $2000, or more if she also filed head of household.  That means a possible penalty plus interest of over $2100 on top of the $2000 tax owed, plus similar amounts for other years.

Good luck.