You retain voting rights of the last jurisdiction you lived in within the US (states or territories) after moving abroad.
So a Californian that moves to, say, Germany can still vote by mail as though they were in California.
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You're mostly correct about the loss of welfare benefits, though. The only exception being that you do remain eligible for Social Security retirement, although some people may not consider that "welfare".
A Puerto Rican in California is entitled to all the benefits of US Citizenship whereas a Californian in Puerto Rico is not. Mostly these are related to welfare and elections. This would be the case for the Californian or Puerto Rican living anywhere in the world outside the US.