It follows a legal challenge brought by the family of one of the victims.
The PPS said in 2021 that it was seeking to drop the case after reviewing the evidence.
But the High Court has said that decision should be reconsidered.
It said it may be for the trial judge to rule on the issue of whether key evidence was admissible or not.
Solider F had been facing trial for the murders of William McKinney and James Wray, plus five counts of attempted murder, in Derry on 30 January 1972.
In her ruling, Lady Chief Justice Dame Siobhan Keegan said the PPS must reconsider its decision, which it based on concerns over the admissibility of evidence in the case.
She said: “We consider that the decision crosses the threshold of irrationality where it simply does not add up, or in other words there is an error of reasoning which robs the decision of logic.
“It follows that the matter should remain with the PPS to reconsider the decision”.
However, a separate legal bid to overturn the PPS’s decision not to prosecute five other soldiers for the deaths of six people on Bloody Sunday failed.
Thirteen people were shot dead and at least 15 others injured when members of the Army’s Parachute Regiment opened fire on civil rights demonstrators in the Bogside – a predominantly Catholic part of Derry – on Sunday 30 January 1972.
The day became known as Bloody Sunday.
It is widely regarded as one of the darkest days of the Northern Ireland Troubles.
William McKinney’s brother Mickey said he was delighted for his own family and for the family of Jim Wray.
“It was with regret that we were forced to bring these proceedings in the first place but the PPS did not engage with us properly in respect of its decision making, but in fact came to Derry last July and presented us with a determination it had already decided upon,” he said.
Mr McKinney told BBC Radio Foyle there was now an onus on the PPS to reconsider their decision.
He said the family and their legal team would “wait and see what happens”.
Solicitor Ciaran Shiels, who represents a number of the Bloody Sunday families, said the PPS must “move immediately to re-institute the proceedings against Soldier F and to secure his committal for trial in the Crown Court”.
“The families continue to be vindicated in their long pursuit of justice,” he added.Tags: