Killer Robert Cairns has been found guilty for the third time for the brutal murder of cancer sufferer Justin Hayward.
Cairns was convicted first in 1998 and again in 2000 after a retrial.
Three judges at London's Court of Appeal have now dismissed his appeal against conviction.
The 28-year-old was jailed for life for stabbing Justin to death on Brighton seafront.
The 19-year-old victim, recovering from treatment for leukaemia and trying to make his own way in life, was found with 40 stab wounds to his neck, throat and eyes.
He was murdered because his killer wanted his drink.
Detective Constable Clinton Novell, involved in the case since it began in 1996, said: "Justin's family is greatly relieved this is concluded and justice has been done.
"This was a shockingly brutal assault on an innocent young man who was suffering from leukaemia and unable to defend himself."
At the original trial in 1998, Cairns' co-defendant Paul Maynard was jailed for three-and-a-half years after being found guilty of causing grievous bodily harm with intent.
He was cleared of murdering Justin and is free.
During the original trial, both had blamed each other for Justin's murder. The jury in the retrial heard how the tragedy unfolded on the night of October 19, 1996.
Cairns, then 23, Maynard, 21, and Justin were all living in the Royal Promenade Hotel in Percival Terrace, Brighton.
Cairns and Maynard had told another resident they were angry because Justin would not share his alcohol.
Cairns said to Maynard something like: "I think we should go ... and give him a slap and rob his beer."
Justin's body was found by passer-by. A Swiss Army-type knife, which had been washed, was later discovered in Maynard's room.
Justin's life was cut short just months after he had undergone nine months of treatment for leukaemia and been told he was in remission.
He came from Copthorne, near Crawley, went to Holy Trinity School, Gossops Green, and was a keen sportsman.
Cairns had checked in to the hotel a few days before Justin.
Born in Dublin, the third of eight children, he moved to London with his family when he was a child.
His father left home while Cairns was a teenager and Cairns's mother returned to Ireland. He was placed in the care of social services.
He arrived in Brighton in early October 1996, where he met Maynard, from the Midlands.
Family and friends of Justin declined to comment on the decision.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article