Apple, he told anyone who would listen, should give shareholders a special dividend, beyond the $2.65 a share it is already paying, in the form of a so-called “perpetual preferred stock.”

He also urged shareholders to vote against an amendment in Apple’s proxy statement that would “eliminate ‘blank check’ preferred stock.” And to drive home his point, he filed a lawsuit against Apple that would make it easier to vote its amendment down.

If he was hoping to get Apple’s attention, he succeeded.

Roughly half an hour before the markets closed, the company issued a statement that contained this key passage:

“We find ourselves in the fortunate position of continuing to generate large amounts of cash, including $23 billion in cash flow from operations in the last quarter alone.

“Apple’s management team and Board of Directors have been in active discussions about returning additional cash to shareholders. As part of our review, we will thoroughly evaluate Greenlight Capital’s current proposal to issue some form of preferred stock. We welcome Greenlight’s views and the views of all of our shareholders.”

That did the trick. The stock popped. In the space of 20 minutes, Apple’s shares jumped from about $455 to $470 — their highest point since Jan. 23, the day the company reported its holiday quarter earnings.

Apple closed at $468.22, up $13.52 (2.97%) for the day.

Below the fold: Apple’s statement in full.

By early last year, Apple’s cash balance had built to a point beyond what we needed to run our business and maintain flexibility to take advantage of strategic opportunities, so we announced a plan to return $45 billion to shareholders over three years. As of next week we will have executed $10 billion of that plan.

We find ourselves in the fortunate position of continuing to generate large amounts of cash, including $23 billion in cash flow from operations in the last quarter alone.

Apple’s management team and Board of Directors have been in active discussions about returning additional cash to shareholders. As part of our review, we will thoroughly evaluate Greenlight Capital’s current proposal to issue some form of preferred stock. We welcome Greenlight’s views and the views of all of our shareholders.

As a part of our efforts to further enhance corporate governance and serve our shareholders’ best interests, Proposal #2 in our proxy includes some recommended changes to our articles of incorporation. These changes were recommended independently of Greenlight’s proposal and would not preclude Apple from adopting their concept. Contrary to Greenlight’s statements, adoption of Proposal #2 would not prevent the issuance of preferred stock. Currently, Apple’s articles of incorporation provide for the issuance of “blank check” preferred stock by the Board of Directors without shareholder approval. If Proposal #2 is adopted, our shareholders would have the right to approve the issuance of preferred stock. As such, Proposal #2 has the support of many of our shareholders.

We remain committed to having an ongoing dialogue with our shareholders to get perspectives around return of capital and driving shareholder value.