Use its completion handler property.
From Apple's documentation:
completion handler
The completion handler to execute after the activity view controller is dismissed. @property(nonatomic,copy) UIActivityViewControllerCompletionHandler completionHandler Discussion When the user-selected service finishes operating on the data, or when the user dismisses the view controller, the view controller executes this completion handler to let your app know the final result of the operation. Availability Available in iOS 6.0 and later. Declared In UIActivityViewController.h