How big does a moon have to be to have the earth locked to it?

I would like a earth-moon system like Pluto-Charon (but with earth instead of Pluto) where both will be tidally locked to each other within something like 3 billion years (before complex life appears). As the moon would probably lock to earth before the opposite it depends only on the mass of the moon so how big has it to be? Is the slowing rate linear to the mass? Is this stable and fast would they spin if it does ?

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How big does a moon have to be to have the earth locked to it?

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