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This is using Zextras Zimbra add-on for mobile device support.
Synchronizing your default Contacts folder is easy and does not require this app to be installed.
If you need to synchronize a shared contacts folder, you can use the CardDAV-Sync Android app. The free version seems to work well on a Samsung S20 phone.
https://play.google.com/store/apps/details?id=org.dmfs.carddav.sync
In the Zimbra Web Client:
ZWC → Contacts (tab) → <your shared contacts folder> (drop list) → Share Contacts Folder