the HP z620/z820 systems are no longer under HP warranty, and have not been for quite a few years however some systems may have a extended warranty agreement still in place, although you can no longer buy a extended warranty for these systems
Z800
EoL: December 2012
EoS: April 2018
Z820
EoL: May 2016
EoS: May 2021
tell your client to call hp support and ask them since he refuses to believe you
and for those who have these systems here's a link to check warranty status
https://support.hp.com/us-en/product/hp-z820-workstation/5225041
EOL disassembly/disposal of 620/820 systems
reply by HP rep on EOL status