By Michael Flaherty

NEW YORK (Reuters) - Activist shareholder Starboard Value LP on Monday disclosed a 4.6 percent stake in Perrigo Co Plc <PRGO.N> and said the Dublin-based drugmaker must make immediate improvements to turn around its sagging stock price.

Shares of Perrigo, whose market capitalization is around $13 billion, surged 7.3 percent to $95.15 in midday trading.

The hedge fund delivered a scathing letter to Perrigo's chief executive officer, John Hendrickson, and its board on Monday, criticizing their performance since the company spurned a seven-month takeover effort by generic drug maker Mylan NV <MYL.O> late last year.

Perrigo acknowledged receiving the letter and said it was looking forward to a "constructive and productive dialogue" with Starboard.

Hendrickson replaced longtime CEO Joseph Papa, who left to head Valeant Pharmaceuticals International Inc <VRX.N> in early May. Since then, Hendrickson has cut earnings expectations twice and said the company suffered during Papa's battle with Mylan.

Papa, in the summer of 2015, convinced investors that they would be better off refusing Mylan's $205-per-share cash-and-stock offer, saying they could earn more if Perrigo stood alone.

"Unfortunately, since that time, results have gone decidedly in the wrong direction, and management's promises have been woefully unfulfilled," Starboard said.

Starboard said the drugmaker should consider hiring an investment bank for advice on selling non-core assets or broader strategic alternatives.

The letter identifies Perrigo's prescription pharma business, known as Rx Pharmaceuticals, as one that would be attractive to other companies. It also said Perrigo should consider selling its stream of royalties from the drug Tysabri, used to treat multiple sclerosis.

"The most likely angle is to drive a sale of both Rx/Tysabri, which could then lead to strategic interest in standalone Consumer," said RBC Capital in a research note on Monday. RBC has a "sector perform" rating on the stock.

At a healthcare conference on Monday hosted by Morgan Stanley, Hendrickson said he has been reviewing all of Perrigo's businesses for potential divests since starting his new role earlier this year.

He said that Tysabri was among the non-core assets that he was open to divesting, but he had not yet made a final decision. He added that a decision would be made soon.

Hendrickson said he considers Perrigo's generics business core and that there are reasons for it to coexist with the over-the-counter business.

Starboard often pushes for board representation and has started more campaigns this year against companies than any other activist shareholder, according to Thomson Reuters data.

Starboard is currently seeking to control the board of another pharmaceutical company, Depomed Inc <DEPO.O>, which successfully resisted a hostile bid from Horizon Pharmaceutical Corp <HZNP.O> last year.

Starboard's letter also criticized Perrigo's management for spending $100 million to thwart Mylan's bid and for receiving bonuses for its successful defense while the company's stock has dropped 50 percent since the offer.

The fund acknowledged Hendrickson's brief role as CEO but pointed out his long tenure at the company and indicated it would not be patient in awaiting a more detailed plan for changes.

(Additional reporting by Natalie Grover in Bengaluru, Caroline Humer and Carl O'Donnell in New York; Editing by Will Dunham and Nick Zieminski)