No, he can't. That's exactly what the lower 30% limit is on — gifts of appreciated capital.
If he sold the shares first, he could claim up to the higher 50% limit. But he'd owe capital gains taxes on the sales, which is almost certainly more than the additional deduction.
He can only deduct up to 30% of his AGI, but also by giving the shares to a foundation he does not realize any of those gains. So the entire donation effectively becomes tax free.
This isn't responsive to earlier comments in this thread and doesn't support (or retract) your earlier wrong statement.
You previously stated, "Bezos can avoid that limit," with "that" referring to either OP's or my statement about AGI deductibility limits, which is incorrect.
I think you might now be trying to make a statement about being able to claim capital gains as an AGI deduction without paying taxes on those capital gains? Which is true enough, but not responsive; it's just a fact that was never in dispute.
If he sold the shares first, he could claim up to the higher 50% limit. But he'd owe capital gains taxes on the sales, which is almost certainly more than the additional deduction.