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At the time, the functionality only worked for mobile web users or BlackBerry and Android devices, but that's no longer the case. Now iPhone users who update to the latest version of the app — version 1.4.3 — can share their Foursquare activity on Facebook too.
You won't notice the new functionality in the app itself; the Facebook sharing is actually enabled and configured from the settings panel of the Foursquare website. The process is no different than for the other devices, so you'll need to allow Facebook to access and publish your Foursquare activity, and once you do, you can choose to share check-ins, mayorships and unlocked badges.