Not sure about choosing the video from the photo library but this works for sending video from an array
NSString *videoPath = self.arrayVideoPaths[self.videoIndex];
NSURL *data = [NSURL fileURLWithPath:videoPath];
NSArray *activityItems = [NSArray arrayWithObjects:data, nil];
UIActivityViewController *controller = [[UIActivityViewController alloc] initWithActivityItems:activityItems applicationActivities:nil];
[self presentViewController:controller animated:YES completion:nil];