Did a territory keep it's independence after an imperialist country annexed it? explain.

The short answer to this would be no.

Specially if you consider that most of those colonies are now countries with a holiday for their independence day (such as USA and Brazil). Such independence was usually achieved by misconduct and continuous armed conflicts. Most countries literally fought for their independence and therefore they can't be considered independent while their were "annexed".

Also, you can check that, even today, after the USA adhered to the imperialist behavior, they annexed countries like Puerto Rico and they are not independent at all.