STATEN ISLAND — A Staten Island married couple were charged with fraud for taking more than $750,000 in Build it Back (BIB) funds after falsely claiming a home they no longer lived in was their primary residence when Hurricane Sandy hit nearly five years ago, federal prosecutors said Thursday.

Nagway Elsilimy and Ahmed Arafa, both 59, obtained $16,626 through federal FEMA funds and $750,719 from Housing and Urban Development through the BIB program after first applying for disaster relief funds in October and November 2012 by claiming their primary residence at 6 Topping St. in New Dorp Beach was damaged during the storm, according to court papers. The couple had actually moved out of the house at least seven months earlier, prosecutors say.

“Taking advantage of funds intended for disaster relief misappropriates taxpayer dollars, reduces monies available to true victims and erodes public confidence in relief programs,” acting Brooklyn United States Attorney Bridget Rohde said.

“This office will continue to work with our law enforcement partners to root out such alleged illegal behavior.” The couple had been living at a separate address on Wellington Court in Heartland Village since at least March 2012 and their old home had been left vacant, according to prosecutors.

The couple, who have three children, continued to receive money through January of this year, most recently getting more than $17,000 in temporary housing assistance funds while they lived at their Wellington Court home.

Investigators said they caught on to the scam after interviewing neighbors who told them the family had moved out months before the October 2012 storm hit and the residence had been left empty, according to court documents.

At one point neighbors called the FDNY after smelling gas at the residence and responders had to shut down a gas line in the home.

Investigators then obtained the lease singed at their current home and spoke with their landlord.

The BIB program has been plagued by problems, including residents being kicked off a list to have their homes elevated and years-long delays in rebuilding homes.

Elsilimy was arrested Thursday morning and was expected to be arranged in Brooklyn Federal Court. A spokesman for prosecutors declined to comment when asked if Arafa was expected to turn himself in.

A lawyer for the couple did not return an immediate request for comment.