When a fixed address is assigned to this machine using DHCPv6, the DHCP server identifies this machine by the DUID (DHCP Unique Identifier) and the specific network interface of this machine by the IAID (Identity Association Identifier) to assign an IP address.
You can check the machine's DUID and IAID by selecting [Network] - [DUID/IAID] in administrator mode of Web Connection (or in [Utility] - [Administrator] of this machine).