BM in our case claimed it on her d (with a different father) one year and then claimed it on my then ds (was my step son then) and we claimed it and she had gotten caught the year before when her other ex claimed it and the IRS went after her for that money. Had she tried it again I would have reported her, especially b/c in writing she asked us to fraud the IRS and let her have the EIC and she would let us have her deduction every other year. We told her NO WAY. Luckily it caught up with her anyway. If you can claim the EIC so she gets caught then you can turn her in but just know the IRS is going to go by what your court papers say the custody arrangement is unless you can provide other proof- so even reporting her may do no good if the CO states she is CP and the child resides with her.