Use this to save a video to an album in the phone gallery. The method creates the album if it doesn't exists.

VideoHelper.swift

import Photos

class VideoHelper {
    
    private static func createAlbum(name: String, completion: @escaping ((_ collection: PHAssetCollection?) -> Void)) {
        //Get PHFetch Options
        let fetchOptions = PHFetchOptions()
        fetchOptions.predicate = NSPredicate(format: "title = %@", name)
        let collection : PHFetchResult = PHAssetCollection.fetchAssetCollections(with: .album, subtype: .any, options: fetchOptions)
        //Check return value - If found, then get the first album out
        if let _: AnyObject = collection.firstObject {
            completion(collection.firstObject)
        } else {
            //If not found - Then create a new album
            PHPhotoLibrary.shared().performChanges({
                _ = PHAssetCollectionChangeRequest.creationRequestForAssetCollection(withTitle: name)
            }, completionHandler: { success, error in
                if (success) {
                    VideoHelper.createAlbum(name: name, completion: { (album: PHAssetCollection?) in
                        DispatchQueue.main.async {
                            completion(album)
                        }
                    })
                } else {
                    DispatchQueue.main.async {
                        completion(nil)
                    }
                }
            })
        }
    }
    
    static func saveCompressedVideoToPhoneGallery(url: URL, albumName: String, completion: @escaping ((_ success: Bool) -> Void)){
        VideoHelper.createAlbum(name: albumName) { (collection: PHAssetCollection?) in
            guard let collection = collection else {
                completion(false)
                return
            }
            PHPhotoLibrary.shared().performChanges({
                let assetRequest = PHAssetChangeRequest.creationRequestForAssetFromVideo(atFileURL: url)
                if let assetPlaceholder = assetRequest?.placeholderForCreatedAsset {
                    let albumChangeRequest = PHAssetCollectionChangeRequest(for: collection)
                    albumChangeRequest?.addAssets([assetPlaceholder] as NSFastEnumeration)
                } else {
                    DispatchQueue.main.async {
                        completion(false)
                    }
                }
            }) { saved, error in
                DispatchQueue.main.async {
                    completion(saved)
                }
            }
        }
    }
}