Updates share prices in paragraph 3, shareholder view and background in paragraphs 8-9

By Valentina Za and Elvira Pollina

MILAN, Dec 22 (Reuters) - Telecom Italia (TIM) TLIT.MI has launched a long-awaited plan to convert costly savings shares into ordinary stock after a compensation windfall that will also help the company to resume dividend payments that were halted in 2022.

TIM's 1 billion euro ($1.2 billion) victory in a long-running case over concession fees enables the company to proceed with the conversion it says will simplify its capital structure and governance, cut costs linked to multiple share classes and boost liquidity and the free float of ordinary shares.

The price of TIM's savings shares TLITn.MI jumped by 9% in early trade after the company outlined the terms of the conversion late on Sunday. Those gains slipped to 4.5% by 1040 GMT. The company's ordinary shares were down 2.2%.

Analysts at Intermonte, which advised TIM on the plan together with Goldman Sachs, said the move could cost TIM about 630 million euros.

However, assuming TIM resumes dividend payouts from next year, savings from the scrapping of the more privileged and higher-paying class of shares are projected at about 1 billion euros, Intermonte said.

Davide Leone, whose London-based investment firm is the main holder of TIM savings shares, welcomed the proposed terms as "market-friendly" and said it worked for both types of shareholder.

TIM has called meetings of both ordinary and savings shareholders on January 28 to vote on the proposal.

Poste Italiane, TIM's largest shareholder with a 27.3% holding, supports the conversion despite the dilutive effect on its stake, a person close to the matter told Reuters. The conversion would reduce Poste Italiane's stake to 19.6%.

The Italian post office is studying options to rebuild its stake, including transferring to TIM its phone services business PosteMobile in exchange for shares, sources said this month.

Savings shareholders will be offered one ordinary share for each savings share plus 0.12 euros in cash for voluntary conversion. Any remaining savings shares after the voluntary period will be converted at the same ratio with a smaller 0.04 euro cash adjustment.

($1 = 0.8531 euros)

(Reporting by Valentina Za and Elvira PollinaEditing by David Goodman)

((valentina.za@thomsonreuters.com; +39 02 6612 9526;))