What is the ruling on my action regarding the book I lost, and the possibility of paying its value in cash instead of buying another copy, and the resulting issues concerning shipping costs and dealing with the bookseller and the librarian?

It is understood that the cost of transporting the book was not overlooked in the invoice by mistake, but rather because the book center was obliged to deliver the book, and therefore did not add shipping costs. There is no need to inquire about this cost. The questioner is advised to seek what is lawful without falling into obsessive doubt.