Transferring Lists Between iOS and Mac (pre-2.41)
If you are running an older version of Address Labels i.e. pre-2.41, or if your Mac is running a version of operating system pre-10.15 (Catalina), then data will not be automatically synced via the Cloud. However, transfers are still possible via Dropbox.
AddressLabels for Mac has been written such that it is possible to transfer iPhone/iPad lists to your Mac, and vice-versa. This is performed using the Dropbox backup/restore feature of the app, similar to the way this feature is often used to transfer lists between iPhone and iPad.
Please note: when transferring lists from one device to another, the existing data is overwritten.
Making A Backup
Moving a list from your iPhone/iPad to the Mac app is simple. First follow the steps in Dropbox Backup/Restore to display the backup table and create a new Backup.

Restoring from a Backup
In the example shown, you will see that some of the backups have a .zip extension, others have .z19 extension, and others a .z21 extension. The .zip files will have been created by the old iOS CardLists app. The .z19 files will have been created by either the iOS AddressLabels v5.22 or by the previous Mac AddressLabels version v1.41. The backups created on an iOS device will have iOSStores in the name. The ones created on a Mac will have MacStores in the title. The latest versions of the iOS and Mac app will save the file with a .z21 extension.
It is always advised to run the latest version of Address labels (1.50 on Mac, 5.30 on iOS). The latest versions of AddressLabels can cope with all of the zip types. So, simply select a file, and click the Restore button. You will get a warning about how proceeding will overwrite any existing lists. If you are ok with that – hit OK and restore your list.
Sorry if the following is a bit complicated, but bear with me. The situation gets tricky if you do not have the latest version of Address Labels running on all devices. Whatever version you are running, you can restore from any of the backups that are seen in the table. However, if you are running an older version on a device, you will not see all of the backups. For example, if you are running the latest Mac version (1.50), and create a backup, the backup file will have a .z21 extension. If you are running the latest iOS version, you will see this backup in the table, and can restore from it. However, if you are running the old iOS version (5.22), it will not display backups with the .z21 extension, meaning you will be unable to transfer the Mac file to your iPad, for example.
Note that if your list uses names from Contacts, and the list was originally created on another device e.g. an iPad, then for the list to look correct (e.g. have correct addresses), you will need to be using the same Contacts on both devices.

To restore from a Backup, click on it to select it, then click the Restore button. You will then see a warning saying that your current lists will be overwritten by the backup. If you are happy to go ahead with this, click OK to do the restore.