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Don't think so sadly, one of the things I really wish we were able to do. D: The most you can do is send out Pokémon from their balls to be out in the field, but you can't feed them once you've caught them.
What is the task name? If it's just something like 'times you've given it food' then all you need to do is throw berries/foods at wild ones and have them eat it, so not your own.