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This is certainly possible. What you need to do to publish to a page is in Publishing Manager to set up a new publish connection to Facebook. Authenticate it with the Facebook user name that you use to manage your page and in the Facebook Album section choose "Non-User Album". The popup next to it will now show all your Pages' albums and you can directly publish to those as a result.
Here this shown on a fresh catalog (my main one is all set up already)