The Historical Enquiries Team has said it supports the findings of the original RUC investigation into the death of a 12-year-old girl killed by the British Army.
Majella O'Hare from Whitecross was on her way to church on 14 August, 1976, when she was hit in the back by a bullet.
Private Michael Williams was charged with manslaughter after the RUC's investigation, but was acquitted in court.
On Thursday, the HET said it had sent a letter to Majella's mother, regarding its findings and that the final copy of its report would be sent to her in "four to six weeks".
An HET spokesman added:"The original RUC investigation found that Private Michael Williams was not returning fire at a gunman as he claimed and they recommended to Prosecutors that he be charged with manslaughter," he said.
"The Prosecutors agreed and charged him with manslaughter, but he was acquitted.
"The HET supports the findings of the original investigation.
"We also said the RUC investigation was thorough and good."
Sinn Fein MP Conor Murphy said the O'Hare family had been devastated by the killing and the fact that no one had been held accountable had "only added to their pain and suffering over the years".
"I hope that the full HET report is published without delay and I believe that this brings the O'Hare family one step closer to having their calls for an apology answered," he said.