Sounds like she is the custodial parent so she can claim HOH and all that comes with if subject to the divorcé decree.

if they’re both in agreement that she gets to claim the kid, then I wouldn’t worry about the 8832. 

as a practical rule of thumb, right or wrong, the first to file gets the kid’s exemption. If, someone inappropriately claims the exemption, the other party has an up hill fight (paper~file with documentation) to get the exemption back.

edit: i misread the q that she is non-custodial parent… if he’s allowing it, I’d at least try to get something in writing from her and a verbal confirmation from him…. (Just in case she’s lying.