Hello, could I pay for something here in the US in a store and in Puerto Rico can the person pick it up? (of course Costco store)

Hello, they also have the option of delivery, and you could put the address you want but I don't know if they have shipments to Puerto Rico, see on their website

Only online you can do it with withdrawal in the chosen store

I think so, you can buy it online by entering the Puerto Rico store and pay it online, place it in the name of the person you want to pick it up