Minor point but the e-commerce site will not be able to read the cookie from Facebook - it will have a special code snippet on the "thank for your purchase" pag

Minor point but the e-commerce site will not be able to read the cookie from Facebook - it will have a special code snippet on the "thank for your purchase" page. When your browser loads this page it also loads the snippet from Facebook (could be a 1x1 pixel or iframe etc etc) and your browser dutifully passes on the cookie as usual to facebook.com when it loads that snippet (i.e. facebook.com is the third party host) then Facebook's servers log the http request with the cookie ID so they mark that as a successful "conversion" (aka sale). The browser will not make cookies from other sites available to the e-commerce site. There is no chance for the e-commerce site to take a look at what is in the Facebook cookie