I have 1 card in my security stack. My opponent attacks me with a Digimon with <Security Attack +1>, and flips over this card during the security check. Its <Recovery +1 (Deck)> activates, adding a card to my empty security stack. Does my opponent continue the security check?
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Yes, they continue by checking the card that was added to your security stack.
Source: BT1-107 Holy Wave