Is it obligatory for a shipping company to inform its client about the discount it received on shipping after a period of dealing with them at the same old price?

You must offer the discount to the company manager if you are his agent in completing the transaction with shipping companies, because the benefits of the contract accrue to the principal. However, if you are a second party to the contract and you agree with the shipping company on your own behalf, then you are not obliged to do so, and there will be two separate contracts, and you will have the gain and bear the loss in both of them.