This is a fantastic question.  As you'll see in the support article below, the cart session is either saved to a browser session or browser cookies. 
   https://hotcakescommerce....8664636-Admin-Orders    So won't be able to retrieve the cart on another web browser, regardless of the setting.  However, what you're detailing is something I've wanted to implement for a long time now.  I've created an issue for everyone to collaborate on in GitHub.    
https://github.com/Hotcak...merce/core/issues/46    In the meantime, it would be possible to duplicate this behavior on your own by throwing a little bit of extra code in your custom viewset to do the following:   
 [list] 
 [*] Determine if the visitor is logged in 
 [*] If logged in, look for any previous orders (carts) that haven't been completed 
 [*] If an abandoned cart is found, assign the respective cart cookie to the browser session 
 [/list]
 
										Will Strohl, Upendo Ventures 
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