The current version of webmail does not support for the CardDAV protocol.
For synchronization you can try using the SyncML Client application, which in the Lite version allows synchronization of contacts for free.
You can enter the following information in the Server Path
- personal contacts: contacts
- another addressbook created by user: contacts/abook_name
- global addressbook: contacts/corporate
- addressbook shared by domain users: contacts/shared/shared_abook_name
Since 7.4.2016 the application is not fully compatible with webmail synchronization server