* Judge orders review of Khodorkovsky appeal
* Lawyers cautious on chances of lifting conviction
* Former oil tycoon fell out with Putin, Kremlin
By Steve Gutterman
MOSCOW, July 24 (Reuters) - Jailed former oil tycoon Mikhail Khodorkovsky won a rare legal victory on Tuesday when one of Russia's most senior judges ordered a court to review his appeal against his conviction on multibillion-dollar theft and money laundering charges.
Lawyers for Khodorkovsky were cautious about the ruling and said it was still unclear whether it was a technicality or a real advance that could lead to a reversal of his conviction.
Khodorkovsky, once Russia's richest man, fell out with Vladimir Putin's Kremlin and is serving a 13-year prison term near the Arctic Circle.
He was jailed in 2003 and is due for release in 2016 after two politically charged trials brought convictions on financial crimes charges linked to his now-defunct oil company, Yukos.
He and his former business partner Platon Lebedev appealed against their December 2010 convictions in the second trial, but the Moscow City Court rejected that appeal last year and a Supreme Court judge upheld that decision.
The chairman of Russia's Supreme Court On Tuesday overruled that rejection and sent the appeal back to the Moscow court, said Supreme Court spokesman Pavel Odintsov.
Khodorkovsky's lawyers said they needed to know more details about Supreme Court chairman Vyacheslav Lebedev's decision.
"Up until now all courts and judges in this case have issued only shameful and illegal decisions made by others," his legal team said on the website khodorkovsky.ru, suggesting court decisions have been handed down from the Kremlin. "We have no illusions. We will see what comes."
Putin has repeatedly criticised Khodorkovsky, suggesting he was behind murders and that the sentence is lenient. Many rights activists believe it is highly unlikely he will be freed before 2016.
One of Khodorkovsky's lawyers, Yuri Shmidt, said the judge's decision could have applied to only part of the Moscow court's ruling or could involve technicalities that would not affect the conviction itself.
"This decision alone tells us nothing," said the lawyer who led Khodorkovsky's defence in the second trial, Vadim Klyuvgant, according to the Interfax news agency.
Odintsov declined to comment on details or potential consequences.
Supporters say Khodorkovsky, 49, was prosecuted in a Kremlin-orchestrated campaign to punish him for challenging Putin, then in his first stint as president. They say it was also aimed to warn tycoons against involvement in politics and increase state control over lucrative oil revenues.
After his arrest and jailing, Yukos was bankrupted by back tax claims and auctioned off with its main production assets ending up in the hands of state-run Rosneft, now Russia's biggest producer and headed by close Putin ally Igor Sechin. (Additional reporting by Maria Tsvetkova; Editing by Alissa de Carbonnel and Andrew Heavens)