With regard to a pension for surviving family of a person who, on any day during the period from August 1, 1980 through the day before the date of enforcement of this Act (hereinafter referred to as "the Effective Date"), has the right to receive a pension for surviving family to which an amount to be added pursuant to the provisions of Article 62-2 of the Employees' Pension Insurance Act has been added (limited to a person to whom that pension for surviving family is paid pursuant to the provisions of Article 38, paragraph (1) of that Act), for as long as it continues to be paid pursuant to the provisions of that paragraph, the phrase "additional amount of pension" in Article 38, paragraph (2) of that Act as amended by the provisions of Article 1 is deemed to be replaced with "additional amount of pension and the amount to be added pursuant to the provisions of Article 62-2 of the Employees' Pension Insurance Act prior to its amendment by the provisions of Article 1 of the Act Partially Amending the Employees' Pension Insurance Act, etc. (Act No. 82 of 1980)".