* Teva Pharmaceuticals Industries hires H Lundbeck A/S CEO
* CEO Schultz to address restructuring and debt reduction
* No starting date yet set, arrival as soon as practicable
* Teva shares up 13 pct, Lundbeck's fall 12 pct on news (Adds details, comments from Teva chairman, Schultz)
JERUSALEM/COPENHAGEN, Sept 11 (Reuters) - Teva poached Lundbeck's Kare Schultz as its new chief executive on Monday, handing the drugs industry veteran the urgent task of convincing investors of the struggling Israeli firm's future.
A costly acquisition spree in recent years has saddled Teva with huge debts and eroded shareholder confidence in generic drugs maker, whose stock has dropped by 50 percent since early August when cut its both its forecasts and its dividend.
The first task for Schultz, named CEO after a seven-month search, will be decide whether to maintain Teva as both a generics and specialty drugmaker, split it in two or get out of low-margin, high competition generics altogether.
Schultz said he will develop a joint strategy with the board and management that would address the "various restructuring initiatives" as well as Teva's more than $35 billion in debt.
Teva -- the world's largest generics drugmaker -- is selling off non-core businesses such as its women's health business and European oncology and pain unit to cut its debts.
"There will be a very clear strategy that will be communicated once we're ready to do that," he told Reuters.
Teva's shareholders welcomed the 56-year-old's appointment, with its Tel Aviv-listed shares rising by 13 percent.
But shares in Denmark's Lundbeck fell by over 12 percent as investors digested the departure of both Schultz and Staffan Schueberg, its chief commercial officer, who has also quit.
Teva, which cooperates with Lundbeck on a number of drugs, said no start date has been set for Schultz, adding he will join the company and relocate to Israel as soon as practicable.
The Israel-based company is facing accelerating price erosion in the United States and working out how to reduce the debts it took on to finance the $40.5 billion purchase of Allergan's generics business last year.
Analysts and investors said Teva paid too much for Actavis and that led to the departure in February of CEO Erez Vigodman.
"We need to restore credibility," Teva Chairman Sol Barer told Reuters. "It's early but ... he (Schultz) will dive in and come up rapidly with a strategic plan."
Barer said Teva had "no plans now" to split in two.
Barer and Teva's board have been criticized for taking so long to hire a new CEO.
"We wanted to make sure we got it right," Barer said, noting that Schultz hit all of the board's criteria, including global and pharmaceutical experience.
"Critically, he has successful turnaround experience. At Lundbeck, it was a troubled company and he turned it around and created significant value for shareholders. And, he has significant credibility with stakeholders," Barer said.
Schultz will succeed Yitzhak Peterburg, who will continue as Teva's interim CEO until Schultz takes over.
Schultz had been widely seen as heir apparent at the world's largest diabetes drugmaker Novo Nordisk but quit in 2015 when Novo's former CEO said he would stay until 2019.
He became CEO of Lundbeck in May 2015 shortly and the Danish firm's share price has more than tripled since he took over and returned it to profit by slimming costs.
At Teva, Schultz will also face significant challenges.
The company has put Iceland-based Medis, a supplier of development work to third-party drugmakers, up for sale and is looking to team up with other drugmakers to fund some of its development pipeline.
Its problems also stem in large part from its specialty business. Its blockbuster multiple sclerosis drug Copaxone had contributed much of Teva's revenue and profit, but its patent has run out and now is facing generic competition.
(Additional reporting by Ben Hirschler in London and Abinaya Vijayaraghavan in Bengalru; editing by Alexander Smith)