Schoolgirl Alice Gross was "unlawfully killed" in a sexually motivated attack, an inquest jury has found.
The 14-year-old is believed to have died at the hands of builder Arnis Zalkalns, who had served a prison sentence for murdering his wife in his native Latvia.
On the sixth day of the inquest at the Royal Courts of Justice in London, a jury of eight men and three women announced their "final conclusions" relating to Alice's death.
They found that her death was "consistent with compression asphyxia".
Alice disappeared from her home in Hanwell, west London, on August 28 2014. Her body was found on September 30 after Scotland Yard conducted its biggest search since the July 7 bombings.
Zalkalns was found hanged in a park on October 4 and police said the 41-year-old would have been charged with Alice's murder had he been alive.
After the jury returned with its conclusions on Monday afternoon, coroner Dr Fiona Wilcox read out a list of recommendations she was "highly likely" to make to the Home Office in relation to foreign national cases.
Last week, she told the jury that evidence given at the inquest did not support conclusions that would "imply that any actions or inactions" of the Home Office or police "caused or contributed" to Alice's death.
Alice's father Jose Gross, sister Nina and mother Ros Hodgkiss were present in court as the jury forewoman read out the conclusions reached.
During the proceedings, Ms Hodgkiss read a prepared statement to the jury in which she said the family "remain stunned" that Zalkalns was "not monitored or even known about in any way" after he came to the UK.
Alice's family have called for careful, targeted reform of the system for exchanging information about high-risk offenders across Europe, after the inquest into their daughter's death exposed serious inadequacies.
Responding to the verdict, Alice's parents said: "Like Alice, our family is in favour of freedom of movement and all the good things it has brought to our lives.
"We do not believe that any citizen deserves to be treated differently based on their race or nationality.
"Our only concern has been to ensure that there are fair and proportionate rules governing the movement of serious criminals within Europe, whether that is a Latvian coming to the UK or a dangerous UK citizen travelling abroad."
Alice's family, represented by Liberty, used the Human Rights Act to secure an inquest under Article 2 of the European Convention on Human Rights to investigate what the authorities knew, or should have known, about her murderer and the systems available for authorities to find out about his background.
Liberty says that as a direct consequence of Alice's death, there is now much better and comprehensive information-sharing about criminal convictions across Europe.
When a foreign national is arrested, the Metropolitan Police now automatically perform a background check in his or her home country.
Crucially, the system "remains reactive rather than proactive", says Liberty.
A person with a conviction for a serious violent or sexual offence who comes to the UK still has to be arrested for a further offence before that check is performed.
Alice's family wish to see a targeted, proportionate and proactive system of information-sharing about "the relatively small number of very high-risk offenders who travel across borders, and whose actions can have catastrophic consequences".
Liberty says this would allow authorities to properly fulfil their duty under the Human Rights Act to protect the public, taking advantage of mechanisms already in place in the EU.
Outside the Royal Courts of Justice, Mr Gross said: "As Alice's father, losing Alice has shattered me.
"The pain of knowing I will never see, hear or cuddle her again is unbearable. This inquest has helped me face what has happened and hopefully now I will be able to properly grieve for my beautiful, loving daughter."
Ms Hodgkiss said: "I still find it almost impossible to believe that our lovely daughter has been so brutally taken from us.
"I miss her every moment of every day. I have felt the need to find out as much as I can about how it is possible that she could have been killed in such a horrific way, and to try and change things so that it doesn't happen to anyone else."
Alice's sister Nina Gross said: "I feel that it is sometimes forgotten that Alice was a real person; a kind and loving sister who deserved so much to live a full life.
"Life is broken and cold without her. Regardless of whether legal responsibility can be attributed to the State for Alice's death, I believe the State failed Alice and our family. Alice was not tragic, but what happened to her was."