And you don't need to open Facebook site to do so or open the massive FB apps, simply use your iPhone. And your static location will be sent to FB. LinkCheckIn uses the native settings.app for configuration purpose and it is running in the background.
LinkCheckIn is a free application and requires a jailbroken iPhone to utilize it. That's obvious, since it's listed in Cydia app store, means you need to firstly jailbreak your iPhone -- if your device is running on iOS 5.0.1 B2 firmware, you can jailbreak it using Redsn0w 0.9.9b8.
LinkCheckIn supports iOS 4 or higher, and can be found under BigBoss repository and respiring your iPhone after you have done installing this application.