Doop trait reads:

Once per game, give Doop a double power action to remove a resource or relic assigned to an opposing character within 6 squares and assign it to another opposing character within 6 squares.

What happens when he uses it against someone assigned a battery? My guess is that it would likely help the opponent, since nothing in doop says that the construct is reasigned, so it's likely the battery owner could assign a second construct to his character, mahing it a corps member again...

When Doop reassigns the Power Battery to a different character the Construct will also be transfered to that character.

Official ruling can be found here: http://www.wizkidseventsystem.com/bb....php?f=3&t=757