(Reuters) -At Home Group Inc said on Wednesday it had accepted a sweetened buyout offer of $2.43 billion from Hellman & Friedman, weeks after an earlier bid from the private-equity firm faced opposition from its largest shareholder, and hedge fund Honest Capital. The home-decor chain said the new offer of $37 per share represented a premium of about 21% to the stock’s closing price on May 4, a day before reports of a deal surfaced. The initial offer of $36 per share implied a premium of about 17%. Shares in Plano, Texas-based At Home jumped as much as 3.1% to $36.81, few cents short of the updated offer. Honest Capital wrote in a letter to At Home in May that the initial offer undervalued the chain, given its plans to more than double its stores and the boom in home-decor segment. According to a letter obtained by Reuters, At Home’s largest shareholder, CAS Investment Partners, had also said it would vote against the deal, echoing Honest Capital’s comments. However, At Home said a 40-day “go-shop” period it had negotiated with Hellman & Friedman that allowed it to solicit bids from other potential buyers ended with no new offers. “This price increase represents our best and final offer,” Hellman & Friedman Partner Erik Ragatz said in a statement. Hellman & Friedman will commence a tender offer around June 23 to acquire all outstanding shares of At Home’s common stock, with the chain’s board recommending that all stockholders tender their shares. Honest Capital could not be reached for a comment, while CAS did not respond. Reporting by Praveen Paramasivam in Bengaluru; Editing by Shinjini Ganguli and Vinay Dwivedi Our Standards: The Thomson Reuters Trust Principles.