BOSTON, Oct 12 (Reuters) - Investment firm PrimeStone is pressing medical device maker LivaNova PLC to consider strategic options including selling parts of its business, refreshing its board and hiring a new finance chief, saying such steps could double its share price.

London-based PrimeStone said that years of underperformance required a new strategic direction and that the company should divest its Cardiopulmonary business, sell or close its Heart Valves business, and consider appointing a new board chairman and hiring a new chief financial officer, according to a letter the investment firm is sending to LivaNova's board on Monday.

PrimeStone said in the letter, which was seen by Reuters, that LivaNova's share price could "more than double to $100", adding: "However, to get there, several changes need to take place."

The investment firm is urging the company to focus on its Neuromodulation unit.

LivaNova did not immediately respond to a request for comment.

PrimeStone, founded by three former partners at private equity firm Carlyle Group, said in the letter that it owned roughly 2.2% of LivaNova. The investment has not been previously reported.

The investment firm said in the letter that it has been a patient investor. But it added that total shareholder return for LivaNova investors since 2015 has been -17% compared with a +171% for its peers during that period.

Private negotiations between PrimeStone and LivaNova broke down in August, according to the letter, because LivaNova's board chairman wanted to reach a higher share price through "beat and raise" earnings releases.

LivaNova, which has a market capitalization of $2.4 billion, was created five years ago through a merger of Cyberonics and Storin. In the last 52 weeks, its share price has fallen 28%. It closed trading at $50.06 on Friday.

PrimeStone said in the letter that it expects other shareholders to support its suggestions that could "help restore the Company's credibility and get it on the path of significant value creation."

(Reporting by Svea Herbst-Bayliss; Editing by Pravin Char)