HMRC use a priority framework to decide who gets the child benefit if the parents themselves can't decide. This was legally challenged in 2012, along with whether it was fair that HMRC won't split the payments - HMRC won.
1 - Who gets the benefit now. Where a person makes a claim for a child or qualifying young person and an award has already been made to another person for that child, the person with the existing award has priority.
2 - Person having a child living with them. The person who has the child living with them has priority over any persons who contribute to the cost of raising a young person but does not have the child living with them.
3 - Husband and wife. In cases where a husband and wife reside together, the wife has priority if there is no other deciding factors.
4 - Parents. In cases where one claimant is a parent and the other is not, the parent shall have priority.
5 - Unmarried couples. In cases where the parents reside together but are not married, the mother has priority of entitlement.
If none of those apply, Child Benefit will be paid to the person who was primarily jointly elected by those who are eligible - the holder of the existing or previous claim. If no agreement can be reached, HMRC will maintain the status quo.
The manual doesn't mention any relevance of either parent's financial situation. Infact it advises that any information regarding to finance is removed before the case is assessed, so that it does not prejudice the case.
How long has the claim been in his name? I think that's her only avenue, really. Sorry to be the bearer of bad news.