(CBS News) NEW YORK - Like a lot of 9/11 family members, Charles G. Wolf is pleased with the National September 11th Memorial that has been open for a year, but he is disappointed that the museum planned to accompany it at Lower Manhattan's ground zero is not ready.
"Disappointed and disgusted," said Wolf, who lost his wife, Katherine, when the first hijacked plane slammed into the North Tower of the World Trade Center. She was 40 and worked for the insurance and consulting firm Marsh & McLennan on the 97th floor.
"If you take a look around here, it has been very, very well done," Wolf said of the pristine memorial plaza featuring acre-square reflecting pools filling the voids left by the footprints of the Twin Towers. The bronze parapets of the pools are etched with the names of the nearly three thousand people killed in New York, at the Pentagon in northern Virginia, on the three hijacked planes that crashed into those buildings, and on a fourth plane that crashed in a field in Shanksville, Pennsylvania.
"However, the name does not tell the story, and that's what's missing what's right now," Wolf said.
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The story of that tragic day will be told in a mostly underground museum that was supposed to open this year. Without it, Wolf says, the memorial is incomplete.
"It is absolutely shameful, because this memorial is not just for the families. This memorial is not just for New York or the surrounding area; this memorial is for the world," Wolf said.
On last year's tenth anniversary of the September 11th terrorist attack on America, the memorial opened, and since then, four and half million people have visited it.
But underneath the tree-lined plaza, construction of the museum has stopped due to a financial dispute between the private nonprofit foundation that runs the memorial and museum and the Port Authority of New York and New Jersey, the government-led transportation agency that owns the 16 acre trade center site and oversees its rebuilding, now expected to cost $15 billion.
In addition to the museum, the Port Authority is constructing the 104 floor office tower intended to be the tallest building in the Western hemisphere, rising with its spire to a symbolic 1,776 feet, and a new train station that is particularly a destination for New Jersey commuters. The tower, dubbed One World Trade Center, has commitments from three tenants to occupy half of its 70 rentable floors when it is scheduled to open in 2014. With cost overruns, the price of the tower and train station now exceeds $3 billion each.
Still, Port Authority Vice Chairman Scott Rechler said the agency is concerned about the finances of the museum and the memorial foundation.
"Now, the question is to make sure there's a budget in place long term to deal with what's going to be a $60 million a year operating budget. You know, what's the revenue to fund that?" Rechler said. "We're not really talking about today, tomorrow; we're talking about five years, 10 years, 15 years, 20 years from now."
In a June letter to New York Governor Andrew Cuomo and New Jersey Governor Chris Christie, who jointly preside over the Port Authority, more than 200 9/11 family members called the work stoppage "a betrayal of those who died on 9/11."
The letter accused the Port Authority of "reckless and irresponsible management" and disputed published claims that the foundation may owe the agency millions of dollars.
"This is something we're 'all in' to want to get done, but it's got to get done right," Rechler said. "This is more than a dollar amount of the past construction. It's about do we have the money now to finish where we are, and do we have a plan in place to ensure that the museum can be sustainable financially going forward."
Memorial and museum foundation officials said they can handle their $60 million annual budget, just as they raised $450 million to build the memorial and museum. Foundation officials said the museum was on budget and on time to open this month until the Port Authority halted construction.
Alice Greenwald, the museum director who has been planning this project for six years, said her staff is ready.
"Design is complete. We are building the exhibitions," Greenwald said. "There is a museum ready to be installed and ready to be shared with the public."
The museum is where visitors will see the faces behind the names on the memorial and learn their stories, as well as the stories of survivors, emergency responders, and witnesses. There will be relics of the offices where more than 20-thousand people worked every day, steel beams that held up the twin towers, and personal mementos of those who died.
Greenwald said, "I think that those millions of people every year who come to this memorial deserve the opportunity to see these artifacts, to learn the story. There are children in school now, born after 9/11, for whom this wasn't a lived experience. It's now history. We owe it to them to teach about this so they could learn."
Museum curator Jan Ramirez has been organizing 40-thousand artifacts in the collection.
One of them is the crushed Squad 18 helmet that belonged to David Halderman, one of 343 firefighters who died. Halderman, 40, had been with the FDNY for nine years.
"To the best of our knowledge he was last seen in the North Tower around the 32nd floor," Ramirez said. "Some survivors who got out from other fire companies said they saw him beginning to work his way down -- they were doing last minute checks to make sure there were no civilians on the floor -- and the towers fell."
The parents of Andrea Haberman donated her recovered pocketbook and its contents to the museum.
"Keys to her apartment and her brand new apartment -- she was engaged to be married," Ramirez said.
Haberman, 25, from Chicago, visiting New York on a business trip, was on the 92nd floor of the trade center in the office of Carr Futures. Her dust-covered cell phone is also among the artifacts. After the plane hit, she was unable to call her parents or fiancé or to get out.
"One thing that worried her parents was that she died alone among strangers," Ramirez said. "They connected with other Carr Futures families and discovered that there were a number of calls that were made out from the 92nd floor and some reference to a young woman and trying to calm her, and they took some consolation that she had not died alone."
The unique observations of astronaut Frank Culbertson are also planned for the museum. Culbertson was orbiting Earth in the international space station on 9/11 and noticed a strange plume of smoke emanating from New York City. NASA mission control in Houston informed him of the terrorist attack.
"I know it's very difficult for everybody in America right now, and I know folks are struggling with this and trying to deal with this and recover from it," Culbertson said in a recorded radio transmission. "But the country still looks good, and for New Yorkers, your city still looks great from up here."
"The sense of public service, of empathy, of compassion, of shared grief, of shared responsibility, to help rebuild -- all of that is our story too," Greenwald said. "It's really a museum about 9/12. This is a museum that takes you from this horrific day, this unimaginable loss, and then we move you to the world after 9/11."
Until the museum is finally built, memorial visitors can see only a few 9/11 artifacts encased in a visitor center just off the trade center site.