With the release of Envoy app 2.0.1, the software has added an option to export labels and tags in BIP-329 format. I believe that only exporting works as there doesn't seem to be an import feature.
Here is how you can do that:
* Foundation Devices and Envoy App
Supports exporting labels: Yes
Envoy supports exporting of labels and tags as .json files in BIP-329 format.
How to export labels using the Envoy app:
1. From the Account selection, click on the two horizontal lines on the top left.
2. Click "Backups."
3. Click "Advanced Backups."
4. Select "Export Tags & Labels (BIP-329)" and select a location where you want to save the file.
5. Click "Save."
@Pmalek, above instruction is only for account relevant to Envoy mobile standalone wallet. If account is related to paired Passport device in my case it is Passport Core then there is no option to export/import labels and tags.
Besides, in fact for Envoy mobile standalone wallet there is an option to import labels and tags in BIP-329 format:
1) From the Account selection, tap on the two horizontal lines on the top left.
2) Tap "Backups."
3) Tap "Advanced Backups."
4) Tap "Download Settings&Metadata..."