He's right and wrong. Living in Sweden, you cannot just decide to register to vote in New York City or Minneapolis just because, as you don't meet the criteria to register.
But, once registered, you can vote as an absentee indefinitely from wherever you came from.
I'm not sure how it works in other situations, but I know that a few of my friends who joined the military moved to Texas and New Hampshire, as the military treats you as a resident of the state in which you enter service for tax purposes.
I'll quote briandear more fully: "so while you can just pick a state at random if you want, the fact is that we do not have representation because the representatives from a state represent residents of that state. It is illegal to register to vote in a state in which you aren't resident. To register to vote as an overseas American, you effectively have to commit fraud"
None of that is right. You cannot pick a state at random. The representatives are also there to support the overseas voters and citizens. And you do not need to be a physical resident in the state in order to register to vote overseas in the state. Moveover, registering as an overseas voter is not effectively committing fraud.
So I disagree with you. briandear was wrong on all points relevant to the snippet I quoted. Otherwise, I think your first two lines make the same points I made.
But, once registered, you can vote as an absentee indefinitely from wherever you came from.
I'm not sure how it works in other situations, but I know that a few of my friends who joined the military moved to Texas and New Hampshire, as the military treats you as a resident of the state in which you enter service for tax purposes.