This will save initial copies of the firewall rules.

sudo iptables-save > /etc/iptables/rules.v4
sudo ip6tables-save > /etc/iptables/rules.v6

In /etc/network/if-pre-up.d/iptables enter the following:

/etc/network/if-pre-up.d/iptables

#!/bin/sh
iptables-restore < /etc/iptables/rules.v4
ip6tables-restore < /etc/iptables/rules.v6
exit 0

In /etc/network/if-post-down.d/iptables enter the following:

/etc/network/if-post-down.d/iptables

#!/bin/sh
iptables-save -c > /etc/iptables/rules.v4
if [ -f /etc/iptables/rules.v4 ]; then
  iptables-restore < /etc/iptables/rules.v4
fi
ip6tables-save -c > /etc/iptables/rules.v6
if [ -f /etc/iptables/rules.v6 ]; then
  ip6tables-restore < /etc/iptables/rules.v6
fi
exit 0

Give permission to the scripts:

sudo chmod +x /etc/network/if-post-down.d/iptables
sudo chmod +x /etc/network/if-pre-up.d/iptables

There are slightly different commands used depending on IPv4 or IPv6.

For IPv4 the commands are iptables-save and iptables-restore.

For IPv6 the commands are ip6tables-save and ip6tables-restore.

The generic method of saving iptables rules is to use the command iptables-save, which writes to stdout.

iptables-save > /etc/network/iptables.rules.v4
ip6tables-save > /etc/network/iptables.rules.v6

For IPv4, the output created by iptables-save can then by read on stdin by iptables-restore. Similarly, for IPv6, the output created by ip6tables-save can then by read on stdin by ip6tables-restore.

If on a server, without NetworkManager, a common approach is then to use a pre-up command in /etc/network/interfaces.

/etc/network/interfaces

iface eth0 inet static
        ....
        pre-up iptables-restore < /etc/network/iptables.rules.v4
        pre-up ip6tables-restore < /etc/network/iptables.rules.v6