Final answer:
The store that completes the sale, which is Store A in this case, is responsible for generating the invoice for the pillow.
Step-by-step explanation:
When a pillow is sold by Store A to be picked up at Store B, the location that will invoice the pillow is typically the store that completes the sale. In this scenario, since Store A makes the sale, Store A would generate the invoice. This is because invoicing is generally associated with the point of sale, which is where the transaction is finalized. Store B, acting as a pickup location, would not usually handle the invoicing unless there is a specific arrangement between the two stores for Store B to complete the transaction.