This is a very difficult trip.
There are no trains from Faro to this area.
I am currently traveling but will post a fuller reply within 24 hours
I have now researched this question more fully. It is not an easy trip by Public Transport.
There are no suitable rail services.
The following is the only bus routing I can find at present which includes bus changes in Seville and Zafra.
There is a Damas/EVA bus leaving Faro Bus Station daily at 07:40 arriving in Seville Plaza da Armas Bus Station at 11:30.
There is a bus service leaving Seville Mondays to Fridays at 13:00 operated by
http://www.leda.es
This arrives in ZAFRA at 14:45. There is a departure from ZAFRA at 15:10 arriving at Jerez de los Caballeros at 16:00