In a letter seen by Reuters, Chief Financial Officer Frank Witter told British hedge fund TCI that Volkswagen (VW) had made significant progress in implementing a new structure for the group and the VW brand.

However, Witter also acknowledged that an inquiry by law firm Jones Day into who was responsible for rigging U.S. exhaust emissions tests was dragging on. "We are all frustrated at the time this is taking," he said.

VW commissioned the inquiry from the U.S. law firm last year, but Witter said Jones Day had to be allowed to continue its work into the second half of this year to ensure "no stone (is) unturned in the pursuit of truth".

The letter, dated May 17, was addressed to TCI founder Chris Hohn, who has said Europe's biggest carmaker needs to improve its performance and create a new governance structure.

Last month, VW announced a 4.1 billion euro (3.1 billion pounds) operating loss for 2015 after making huge provisions to cover the cost of clearing up the scandal.

It has reached a nearly $10 billion deal with the U.S. government, but still faces an array of civil law suits and members of its management board - which runs the company day-to-day - are under fire over their bonus scheme.

Asked about Witter's letter, TCI partner Ben Walker said VW had to reduce its labour costs and raise its profitability. Walker aimed his criticism at trade unions and the government of Lower Saxony state, which has a 20 percent stake in VW.

"It's a letter of fine ambitions but the key point is that the unions and, in particular, Lower Saxony have to back the management team now," he told Reuters.

"Then this could be the turning point for Volkswagen. Lower Saxony and the unions have to acknowledge that a successful auto company cannot survive long-term with margins of 2 percent."

NATURAL ATTRITION

VW employs over 120,000 people at six factories in Lower Saxony, including its Wolfsburg headquarters, and the government along with unions have been keen to protect jobs throughout the firm's crisis.

TCI said it had "exposure" to 2 percent of VW's non-voting preference shares and none of the group's ordinary shares. It is therefore dwarfed by the company's dominant shareholders - the Piech and Porsche families, Lower Saxony and the Gulf state of Qatar.

However, Walker said shareholders should back TCI's recommendations - setting tough financial targets, aligning management compensation with shareholders and controlling spiralling labour costs.

"All those key recommendations are clearly shared with all investors, including the families, Qatar and ultimately Lower Saxony," he said, adding productivity could be improved by natural attrition of VW's workforce, and controlling wage inflation and employee growth.

Bonuses for VW's top managers after the 2015 loss have provoked a row which has drawn in German politicians.

VW will pay 12 current and former members of the management board 63.2 million euros in fixed and flexible remuneration for 2015. Management board members have had 30 percent of their variable bonus awards withheld, but this will be released if the share price - currently around 125 euros - reaches 140.

Witter said management incentives and bonuses would also be looked at as part of a process of devising a new strategy 2025, which is due to be announced before the summer.

VW had made progress, including building on the experience of its Porsche sports car brand. "We would like to highlight the introduction of product line management where the best ideas from Porsche are being introduced into the engineering processes of the Volkswagen brand," the letter said.

(Writing by Edward Taylor and David Stamp; Editing by Mark Potter)

By Jan Schwartz and Maiya Keidan