It's not possible, Shawdad; your cart is tied to your computer by what's called a "browser cookie" (a small transient data record stored by your web browser). The link you posted (I removed it) is the SAME link for EVERYONE who has an open cart at that company. If I had open cart at that company, for entirely different products, I'd use the same link as the one you posted. The data in the local browser cookie is what tells the server which 'cart' data set to serve up.
You can post a text list of items, if you like.
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