The sandwich shop operated in the town of Beckley, owned and operated by Charlie. The shop specialized in cranberry sandwiches of which the cranberries were trucked in from an undisclosed location in Cranberry Bog. The shop opened up across the street from Sal Jefferson's shop, Sal's Grinders, and offered exactly the same sandwiches as the existing restaurant. In addition, Sal and Charlie were childhood rivals.
As time passed, Big Papa Moe's Lip Smackin' Sandwich Shack became incredibly popular and the people of Beckley preferred buying their sandwiches from Charlie instead of Sal's. In time, even Sal's employee Grace, who opened Sal's Grinders alongside Sal, left due to the fact that he couldn't pay her anymore, and was hired by Big Papa Moe's.
Sal was determined to figure out why Papa Moe's sandwiches were such a hit and deconstructed the ingredients to determine the root cause of the craze. Eventually, Sal followed the Papa Moe's delivery truck and discovered that the source of the cranberries was from a radiated quarry in Cranberry Bog, proving that Papa Moe's was secretly poisoning their customers and the people of Beckley with irradiated cranberries. Determined to get revenge, he vowed to "let him [Charlie] have it."
Big Papa Moe's Lip Smackin' Sandwich Shack appears only in Fallout 76.