shareVideoToFacebook.m

- (void)facebookLogin {
    if ([[FBSDKAccessToken currentAccessToken] hasGranted:@"publish_actions"]) {
        [self shareVideoOnFacebook];
    } else {
        FBSDKLoginManager *loginManager = [[FBSDKLoginManager alloc] init];
        [loginManager logOut];  //very important line for login to work
        [loginManager logInWithPublishPermissions:@[@"publish_actions"]
                handler:^(FBSDKLoginManagerLoginResult *result, NSError *error) {
                        if(!error) {
                            [self shareVideoOnFacebook];
                        } 
                    }];
    }
}

- (void) shareVideoOnFacebook {
    NSString *videoPath = @"/Documents/.../movie.mov";
    NSData *videoData = [NSData dataWithContentsOfURL:[NSURL fileURLWithPath:videoPath]];
    
    NSMutableDictionary *params = [NSMutableDictionary dictionaryWithCapacity:3L];
    [params setObject:videoData forKey:@"video_filename.MOV"];
    [params setObject:@"Title for this post." forKey:@"title"];
    [params setObject:@"Description for this post." forKey:@"description"];

    [[[FBSDKGraphRequest alloc] initWithGraphPath:@"/me/videos" parameters:params HTTPMethod:@"POST"]
     startWithCompletionHandler:^(FBSDKGraphRequestConnection *connection, id result, NSError *error) {
         if (!error) {
             //video posted
         }
     }];
}