Walter Carver will now collect the entire $10,000 prize that he won in 2007. PHOTO: Debbie Egan-Chin

 A 69-year-old Vietnam vet from Brooklyn can finally enjoy all his 2007 lottery winnings.

The Court of Appeals ruled Thursday that state officials were wrong to claim half of Walter Carver’s $10,000 lottery jackpot.

But now the veteran, who shovelled snow and sorted mail for 35 hours a week on the Work Experience Program, has finally won an appeal to challenge the ruling.

Walter Carver, 65, won $10,000 on a $2 scratch card in 2007, but had the winnings confiscated by New York state.

“We are thrilled,” said Carver’s attorney Susan Antos. “This has been a long battle.”

Because Carver received public assistance through a welfare-to-work program from 1993 to 2000.

The state claimed it was entitled to appropriate half of his winnings from the scratch-off lottery ticket as a reimbursement for the benefit payments.

The ferry terminal where Walter Carver worked as a janitor. PHOTO: Dwayne Bent

Carver challenged the move in court, arguing that because he worked for the benefits he should be treated as an employee and afforded federal minimum wage protections.

The state’s interception of the lottery money, Carver argued, meant he was effectively paid below minimum wage for the work he performed for the government.

Carver, who lived with his brother in Gerritsen Beach at the time, lost his Wall Street clerk job in the early 1990s and received about $150 a month in the welfare-to-work program.

He had to shovel snow, sort mail, sweep sidewalks and do other menial tasks.

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