Shares of Twitter rose about 4% in early Wednesday trading to $40.15.
"We are hopeful that winning the motion to amend takes us one step closer to the truth coming out in that courtroom," said Alex Spiro, an attorney for Musk, in a statement.
Musk's legal team argued on Tuesday that justice demanded delaying the five-day trial so Musk could investigate claims by whistleblower Peiter Zatko, known as "Mudge," that Twitter hid weaknesses in its security and data privacy.
Musk's initial case against Twitter claimed the company misrepresented the prevalence of spam or bot accounts on the platform.
Last month, Zatko's allegations became public and provided Musk, the world's richest person, fresh ammunition to bolster what legal experts said was a long-shot attempt to walk away without paying a $1 billion termination fee.
"We look forward to presenting our case in court beginning on Oct. 17th and intend to close the transaction on the price and terms agreed upon with Mr. Musk," said a statement from Twitter spokesman.
In July, Twitter sued Musk, who is also chief executive of electric vehicle maker Tesla Inc to hold him to his April agreement to buy the company for $54.20 per share. The company has alleged that Musk got cold feet over the deal as global politics and inflation rattled markets soon after the deal was signed.
At Tuesday's hearing, Twitter's lawyer read a message from Musk that came to light during the litigation that the lawyer said showed the billionaire was not actually concerned about spam accounts.
Musk sent a message to a Morgan Stanley banker in May, as Russia's President Vladimir Putin was warning the West over his country's war in Ukraine, that read "it won't make sense to buy Twitter if we're heading into World War III." The deal contract allows Musk to walk away under certain narrow conditions, although a war is specifically excluded.
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