Is it reported on a 1099?  Issued by the publisher?  So she is not receiving them from her ex, she is receiving them from a third party because he has assigned them to her?  Many years ago I worked on a case involving royalties from one of the members of the Eagles ("Hotel California") that were assigned to his ex-wife.  The court said he could do that.  Normally, "assignment of income" is not recognized, but patents and copyrights are different.  It doesn't make much sense to put them on Schedule E, along with minerals and fossil fuels, but that's what IRS says to do.  Use your own judgment on how much depletion she should claim.