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I wouldn't trust or recommend any non-Apple battery, due to the number of problems reported with "knockoff" batteries. Also, there is no assurance that knockoff batteries have the same charging technology that Apple uses, involving the battery, the MagSafe adapter and the Mac's logic board.

Battery Replacement
Replacing the built-in battery in your MacBook Pro
Replacing the Battery in your MacBook Air
Intel-based Apple Portables: How to replace or service a built-in battery

The link below should answer most, if not all, of your battery/charging questions. If you haven't already done so, I highly recommend you take the time to read it.
 
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