STOCK MANAGEMENT

I need a stock management aplication / module. I have one main prestashop account. The module must be able to sync stock with multiple ebay accounts, one amazon account, one fnac account, one rakuten account, and other prestashop stores. Image like how it should be i have added in description. For ebay, having multiple accounts, for example account 1 will have item number 1234325621 and account 2 will have item number 5628734873, same item with different names. Must be able to sync stock by inserting item numbers in prestashop. For example: Samsung galaxy S3 battery has item number 54378968768 from account 1 and item number 5837487283 from account 2. When it is no stock, the module must set availability to zero in all accounts. Also, when a item sells in any account, amazon, ebay, fnac, prestashop, module must manage stock, remove 1 quantity from the rest of the accounts.