The President shall provide for the presentation of the Medal of Honor Flag designated under section 903 of title 36 to each person to whom a medal of honor is awarded under section 7271 of this title. Presentation of the flag shall be made at the same time as the presentation of the medal under section 7271 or 7282(a) of this title. In the case of a posthumous presentation of the medal, the flag shall be presented to the person to whom the medal is presented.