The birth family of Elsie Scully-Hicks have said she would "still be alive today" if she had not been removed from their care by social services.
Matthew Scully-Hicks, 31, was jailed for life and ordered to serve a minimum of 18 years in prison for murdering Elsie just two weeks after formally adopting her.
Scully-Hicks, of Delabole, Cornwall, showed no emotion as judge Mrs Justice Nicola Davies described how he had murdered 18-month-old Elsie at his home in Llandaff, Cardiff in May 2016.
Cardiff Crown Court heard he struggled to cope with Elsie, describing her as "Satan dressed up in a Baby grow", "a psycho" and "the exorcist" in text messages.
Mrs Justice Davies, when sentencing Scully-Hicks (pictured), took into account a victim impact statement - which was not read in court - provided by Elsie's birth family.
In the statement, which can now be reported following an application by the Press Association, Elsie's natural family said they were "numb with pain".
Elsie was named Shayla O'Brien by her birth family when she was born in November 2014.
Speaking on behalf of the family, Elsie's birth grandmother Sian O'Brien said: "I accept that at the time of giving birth my daughter was living a chaotic lifestyle and was not in a position to care for Shayla and she was removed from the hospital five days after birth by social services.
"As a family, we continued to have contact with Shayla whilst she was in the care of the foster family."
Ms O'Brien said all of Elsie's family were "extremely attached to her and loved her very much".
She said: "In January 2015, I started proceedings in the family court to become the legal guardian for Shayla.
"I wanted to bring her up in a happy, healthy and warm family environment, that was all taken away from me when social services and the family court decided I would not be able to cope."
A decision was made that Elsie, who was renamed by her future adoptive parents Matthew and Craig Scully-Hicks, would be put up for adoption in May 2015.
The statement continued: "We all continue to fight on even though every day we are numb with pain and hurt deep in the knowledge that Shayla was loved unconditionally by us all as a family and knowing that had she not been taken away from us, she would still be alive today."
"Despite this decision and Shayla being in foster care, we as a family were still able to have weekly contact with her and we saw her without fail at every opportunity," Ms O'Brien said.
"In August 2015, out of nowhere, we were told by social services that we had to go and see Shayla as soon as possible and say goodbye for the final time as a suitable adoptive family had been found for her.
"This was completely devastating for us all."
Ms O'Brien said the family hoped that one day the little girl would be reunited with them but were visited by social services in January 2017.
The family were informed that Elsie, who suffered bleeding in her brain and eyes, a fractured skull and fractured ribs, had died in May the previous year.
"In itself this was devastating news but to then be informed that one of the parents who had adopted her had been charged with murder and was allegedly responsible for her death was completely incomprehensible," Ms O'Brien added.
"A person who had been deemed by the authorities to be a fit and proper person to bring up my granddaughter was responsible for her death, and they took her from me telling me I would be unable to cope."
Scully-Hicks, a fitness instructor and former lifeguard, struggled to cope with being the primary carer for Elsie as his husband, Craig Scully-Hicks, 36, worked full-time.
The little girl suffered a catalogue of injuries - including bruises and a broken leg - during the eight months Scully-Hicks had looked after her.
She died four days after being violently shaken and sustaining a fractured skull in May 2016, which was just two weeks after being formally adopted.
Jurors were told that social workers and a health visitor visited the family home 15 times from when Elsie was placed with the defendant to her death.
Scully-Hicks insisted he never harmed Elsie and claimed she must have spontaneously suffered fatal injuries after he changed her for bed at home in Llandaff, Cardiff.
But following the trial lasting more than four weeks, during which 12 medical experts and six doctors gave evidence, jurors unanimously found him guilty of murder.
Passing sentence, Mrs Justice Davies described Elsie "as a young, vulnerable and defenceless child" who Scully-Hicks had previously injured.
"In deliberately inflicting serious injuries upon your 18-month-old adoptive daughter you abused the trust which had been placed in you as Elsie's adoptive father. It was a gross abuse of that trust," she said.
"It was an abuse of the responsibility which had been placed upon you as her adoptive father to protect and care for this young, vulnerable and defenceless child.
"Your actions in killing Elsie have devastated three families - the birth family of Elsie, the family you had sought to build with Craig Scully-Hicks and your own birth family."
The judge added: "You were living in comfortable social circumstances with the close support of professional agencies, your husband and wider family.
"To those who saw you regularly, be it healthcare professionals, social workers or friends and family you were a loving and caring father.
"The difficult times were when you were alone with Elsie or with her and her adoptive sibling.
"You deny being unable to cope with two children but the texts indicate otherwise. You are an intelligent man. You would have known you were struggling to cope with Elsie.
"You knew that in November and December your frustration and anger towards Elsie had resulted in injuries to her.
"You told no one the truth of what had occurred nor the reason for it. Regular visits were made by social workers and the health visitor.
"To no one, not even your husband, did you have the courage to speak of your difficulties. You put your own self-interest before that of the young child you had been entrusted to protect.
"To Craig and the professionals you continued to present as a concerned, caring and loving father.
"What people did not see or hear, because they were not in the house at the time, was the frustration and anger which you were demonstrating because of your inability to cope with your young adoptive daughter."
An independent Child Practice Review is now under way to examine the "tragic circumstances" of Elsie's death, a spokesman for Cardiff and Vale of Glamorgan Regional Safeguarding Children Board said.
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