Get your taxes done using TurboTax

No.  Your ex's GF cannot claim your son.   Your son is not related to the GF so she cannot claim him unless he lived with her all year.   If you are the custodial parent, then as far as the IRS is concerned you are the one who can claim your child.  Whether you claiming him would result in your ex taking you to court is questionable.  But their plan to have GF claim him won't fly.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**