Paul Gilligan's father Dennis, 64, told The Sun: "It's disgusting. Losing his freedom was part of the punishment. We have lost contact with Paul forever but he can still contact his family and friends."
A Prison Service spokesman said the page would be taken down.
He added: "Prisoners have no access to the internet and are barred from updating Facebook.
"It's an offence to have a mobile in prison. We work hard to keep them out."