Not exactly accurate.
Anyone can claim anyone else on a tax return; whether or not it is legal is the question.
The mother does not have the right to claim the child unless one of the exceptions stated earlier apply. If she does claim the child and no one else does, it is unlikely that any consequences will come of her actions. You may report her using this form: http://www.irs.gov/pub/irs-pdf/f3949a.pdf ---but the IRS has bigger fish to fry and I have never seen them respond to this type of reporting tactic.
A better way to "thwart" the mother's actions would be to have your boyfriend file his own return, and claim himself and the child. Even if he has no income, he is allowed to file an information return. This way, the child's social security number will show up on the return. If he does this before the mother and files electronically, and she also claims the child and files electronically, then her return will be rejected.
If you do not want to give up your boyfriend as a dependent (if he meets all the tests for you to claim him), then your boyfriend may file a return as a dependent, and include form 8901, claim for child tax credit: http://www.irs.gov/pub/irs-pdf/f8901.pdf .
This form can be used to claim a qualifying child for the child tax credit benefit, if the taxpayer is the dependent of someone else (your dependent). Even if he has no income, he will not get any money from the child tax credit, but the child's SS number will be associated with this tax benefit and make it more likely that there will be an investigation if the mother claims the child. If he files his return electronically this way before she files hers, it is also possible that her return will be rejected. You do not need HR Block to file your return this way, you can use a software product, or use IRS freefile service, available Jan 16: http://www.irs.gov/efile/article/0,,id=118986,00.html