However, the amount of the reimbursement shall be determined in the manner prescribed in subsection (b) for an interment, but may not be larger than that authorized when the United States provides the grave site. A claim for reimbursement under this subsection may be allowed only if it is presented within two years after the date of death or the date the person who would have been designated under subsection (c) to direct disposition of the remains, if they had been recovered, receives notification that the member has been reported or determined to be dead under authority of chapter
10 of title
37, whichever is later.