More homeless families will move into an Upper West Side building being converted into a shelter as soon as possible, city officials said, following a judge’s dismissal of a lawsuit fighting the West 94th Street facility.

Manhattan Supreme Court Judge Lyle Frank dismissed the suit brought by a neighborhood group and current tenants of 306 W. 94th St. — formerly known as “The Alexander” — a seven-story former residential hotel built in 1910, according to court documents filed Monday.

Frank tossed the suit, saying those who brought it — the group Neighborhood in the Nineties and four current tenants of the West 94th Street building — did not prove claims the city violated zoning and city law at the shelter site.

About 75 homeless families already live in the shelter, following another judge’s partial go-ahead for the shelter conversion at the building after the groups filed suit in mid-December.

The city Department of Homeless Services has been waiting to fully utilize the building since the agency announced in the fall of 2018 the site would open as a replacement for the notorious Freedom House shelter on West 95th Street.

Department spokesperson Isaac McGinn said the agency is working with the state to get final approval to move in the remaining residents. In total the shelter, run by Praxis Housing Initiatives, will house 220 homeless New Yorkers.

McGinn called the ruling “a win for families experiencing homelessness.”

“We remain committed to working with the community to ensure this facility is seamlessly integrated into the neighborhood and that these families receive a warm welcome,” he said in a statement.

Aaron Biller, president of Neighborhood in the Nineties, said in an email that he and his fellow plaintiffs are “disappointed by the court’s decision and intend to appeal.”

The decision comes just a week after THE CITY first reported a ruling in the city’s favor at another controversial Manhattan shelter — a facility for homeless men on West 58th Street, adjacent to the so-called Billionaires’ Row.

That shelter and the West 94th Street site are two of 90 new homeless shelters slated to open under Mayor Bill de Blasio’s revamp of the system, which aims to end the use of stand-alone apartments and hotel rooms to house homeless people.

The city’s homeless population remains at record-high levels, according to a recent report by the homeless advocacy group Coalition for the Homeless, with more than 68,000 New Yorkers in the shelter system as of this year.

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