N.H. Rev. Stat. Ann. § 115-A:13

No applications shall be certified for payment unless written evidence is presented indicating that any person or persons herein described as having a prior right to benefits shall have deceased; and provided further that if, prior to the date upon which this subdivision takes effect, benefits have been paid to the father or mother of a qualified person, who at the time had a child or children, the rights or benefits shall not in addition accrue to said child or children as a result of the provisions of this subdivision.