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I was replacing a battery for a customer, and it shorted. The battery was disconnected from the logic board, but when I put a metal spudger under it to pry it loose, the battery sparked and let out smoke. Do you think the battery released residual electricity into the phone’s housing? And if so, will the logic board be ok?

Since logic board iphone has an sensitive component, even electro static could damage those component. Short electricity could make an unpredictable error/damage. For safety work, avoid mistake during handling a sensitive device. Inspect & test all phone function & system when accident occur.