Ian Russell said he was flabbergasted when officials told him the case did not have “wider public interest”.
Mr Russell said he was delighted the Legal Aid Agency – which operates under the Ministry of Justice – confirmed it had reconsidered its decision.
He added: “I would like to thank everyone for the many offers of support we have received. This decision is a weight lifted from our family and we now look ahead to a full and fearless inquest into Molly’s death.”
The coroner overseeing Molly’s inquest has written to Facebook, the owner of Instagram – as well as Pinterest, YouTube and Apple – requesting they hand over all relevant information to the case.
Legal Aid guidelines says funding is not automatically granted at inquests except in “exceptional circumstances”.
Merry Varney, solicitor at Leigh Day, the law firm representing Molly’s family, said: “It is disappointing that our clients had to go through the appeal process to get a positive outcome… and many other families are not successful in their appeals.”
She called for more legal aid funding for inquests, saying many families ended up representing themselves “completely unqualified”.
The Ministry of Justice says it had reviewed the system of legal aid at inquests and changes would make it “more accessible and supportive”.