The Harper government's law to end the registry ordered the destruction of all records of long guns, but Quebec objected, saying it wanted to set up its own registry, using the federal data as a starting point.
The province went to court to preserve the records on Quebec-owned rifles and shotguns.
A Quebec Superior Court ruling in September 2012 sided with the province, but the Court of Appeal reversed that decision.
In November 2013, the Supreme Court agreed to hear Quebec's appeal and ordered that the records be preserved pending its decision.
The records from the rest of the country have already been destroyed.
While the Superior Court found that the federal government could not unilaterally destroy the data, the appeal judges found errors in the reasoning.
They said the federal government was entitled to handle the records as it saw fit.
In its argument before the Supreme Court, the federal government said the records were collected and kept under the sole control of the registrar of firearms, a federal public servant.
"Quebec has no right to the records and cannot demand their transfer in order to create a provincial registry 'as it sees fit,'" the federal factum said.