Yes. Once again, we need to make a clear distinction between the registry for declaration of residency abroad and registration on the electoral list.
For example, businessmen from Singapore and China often settle in Canada. They register on the registry in Canada and must then say whether they want to be added to Canada's electoral list. They are no longer on China's electoral list because they have left the country, but they can still ask to exercise their right to vote in the national territory.
In short, the answer is yes. They must register again. This is also true for the national territory. When a French citizen moves to a different commune in France, the citizen is on a different electoral list.