The 1968 Gun Control Act and subsequent amendments codified at 18 U.S.C. § 921 et seq. prohibit anyone convicted of a felony and anyone subject to a domestic violence protective order from possessing a firearm.
The Second Amendment Permits The Disarming of “Dangerous” Felons. Each year, more than 8,000 people are convicted for unlawful possession of a firearm under 18 U.S.C. § 922(g). About 90% of those cases arose from gun possession by a felon.
A Certificate of Relief from Civil Disabilities is a Certificate issued by a Court or the New York State Department of Corrections and Community Supervision which restores a person's civil right following a conviction. It can also be used to restore a person's firearms rights.
If more than 5 years have passed since completing their prison sentence (including parole or probation), the law allows possessing a firearm at home.
For those with more than one conviction, the court may restore firearms rights two years after completion of sentence for most felonies, or after 10 years for a serious felony (such as murder or sexual assault). For a person convicted of a “dangerous felony” firearms rights may only be restored by pardon.
So long as that person is the sole possessor of the firearm and that the convicted felon is not in a position to exercise control over it, that's fine. For instance, the individual must be carrying a firearm on their person, they cannot keep it in the glove box and have a convicted felon in the car.