Welcome to Android Central! Apps from the old phone can be reinstalled on the new phone from Google Play Store, as long as you're logged in with the same account. However, it can be difficult to transfer the app data over (assuming that data wasn't stored to a cloud server somewhere). It may be possible to access discrete files on the broken phone using this method:
http://forums.androidcentral.com/gen...ed-screen.html. However, copying over data files that seem to be associated with an app won't guarantee that a newly installed version of that app on the new phone will be able to incorporate that data.