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Once you are given access to freely roam around Cell Block A, head to Cell A-305 on the third floor. Beneath the bunk in this room is a crate with a bottle of Old Man's Prestige. Pick up the bottle and now head down to the ground floor of the cell block.

Make your way to the prison yard exit and speak with the inmate standing to the left of the door. He will offer to trade a Multitool in exchange for a bottle of alcohol. Give him the the bottle of Old Man's Prestige and the achievement will unlock shortly afterwards.