A child born to a woman eligible for and receiving medical assistance under a State plan on the date of the child’s birth shall be deemed to have applied for medical assistance and to have been found eligible for such assistance under such plan on the date of such birth and to remain eligible for such assistance for a period of one year. During the period in which a child is deemed under the preceding sentence to be eligible for medical assistance, the medical assistance eligibility identification number of the mother shall also serve as the identification number of the child, and all claims shall be submitted and paid under such number (unless the State issues a separate identification number for the child before such period expires). Notwithstanding the preceding sentence, in the case of a child who is born in the United States to an alien mother for whom medical assistance for the delivery of the child is made available pursuant to section 1396b(v) of this title , the State immediately shall issue a separate identification number for the child upon notification by the facility at which such delivery occurred of the child’s birth.