You might try a web search for
migrate linux user.
Most of the articles, I fear, will be about migrating from one distro to the same distro (though perhaps a newer version), but I think that will be a good starting point.
If I were going to try this, I'd start by moving the contents of my /home, including the dot-config files, being careful to skip dot-config that are not relevant to the new install. For example, if you are moving from KDE to MATE, you would not the konqueror dot-config files, but, if you are using Thunderbird on both machines, you would need your mail store.
I'm not quite sure I follow what you're saying about the external HDD, but it seems to me that, if you are going to move the external HDD from one machine to the other, it should be fairly easy for root to change the ownership with
chown command.
Just a few thoughts.