Elon Musk has filed to complete his $44bn (£38bn) acquisition of Twitter after months of legal drama. Lawyers for Musk confirmed in a court filing on Tuesday that the billionaire will push ahead with the deal after performing another dramatic U-turn on his decision to walk away from the agreement. The filing confirmed reports from Bloomberg on Tuesday that the Tesla chief executive had written to Twitter offering to close the deal at the original price of $54.20 a share, which sent shares in the social media site climbing more than 12% to $47.93 in New York before trading was halted. Musk had been set for a courtroom showdown with Twitter on 17 October, with multiple legal commentators warning he had a slim chance of succeeding in his attempt to scrap the deal. “We write to notify you that the Musk Parties intend to proceed to closing of the transaction,” read the notice, filed by Musk’s lawyers with the Delaware Chancery court which was overseeing the trial. Twitter agreed, writing: “The intention of the company is to close the transaction” that was agreed upon during the original deal. The Wall Street Journal reported on Tuesday that Musk had made the proposal to Twitter’s lawyers overnight on Monday and had filed a letter with the Delaware chancery court before an emergency hearing on the deal on Tuesday. Anat Alon-Beck, a law professor at Case Western Reserve University in Ohio, said Musk appeared to be “finally listening to his lawyers”. Musk was due to be questioned under oath by Twitter lawyers on Thursday and Friday as part of preparations for the Delaware trial. “He will be a fool to not at least try to buy the company now and avoid [a deposition],” said Beck, claiming that Musk “has no defence on trial”. Although Musk’s filing has eliminated the impending trial, the showdown is not over yet, Alon-Beck said. “It’s not like this is going to be cleared up tomorrow,” she said. “The parties still have to approve everything, sign and finalise the deal, and Musk still has to come up with funds to close it.” The deal has been complicated by the fluctuating value of Twitter, which has been heavily influenced by Musk’s antics since announcing the purchase in April. Shares plunged in July after Musk initially backed out, sinking as low as $32 – far from the $54.20 a share value at which he agreed to buy the company. After Musk again reversed course on Tuesday, shares surged 22.2% to $52 (£45.31) – closer to the value agreed upon in the deal. Musk’s initial argument against buying the company was that it had miscounted the number of spam or bot accounts on its platform. Twitter denied it miscounted the number of spam accounts, or vexatious accounts not operated by human users, and said Zatko’s claims were “riddled with inconsistencies and inaccuracies and lack important context”. Twitter has also been scathing about Musk’s behaviour. In its lawsuit demanding he close the deal on the agreed terms, it said Musk’s behaviour was “a model of bad faith” and accused him of treating the sale process as an “elaborate joke”.