Mr Justice Brian McGovern said he was satisfied to appoint Mr Neil Hughes, of Hughes Blake, Chartered Accountants, as examiner to the award-winning company, which runs a restaurant and gourmet food hall in Dublin's Exchequer Street.
Mr Hughes now has until early April to come up with a scheme of arrangement with the company's creditors.
If the scheme is approved by the High Court, it will allow the firm to continue to trade as a going concern.
The company sought the protection of the court on the grounds that it is insolvent and unable to pay a €1.4m tax bill.
However, the High Court heard that an independent accountant's report has said the business has a reasonable prospect of survival if certain conditions are met, including securing new investment.
Lawyers for the Revenue Commissioners said they were taking "a guarded but neutral" stance to the company's application for examinership.
Lawyers for the examiner told the court that he shared the view that the company has a good prospect of survival.
The court was told there have already been 18 expressions of interest by prospective investors in the company.
The court heard no bookings had been cancelled and six further bookings for significant events had been made since the company sought court protection.
Lawyers for Fallon & Byrne said the firm's creditors were supporting the application were either supportive of or were neutral towards the application for examinership.
Counsel said that in the event the company was liquidated there would be a deficit of more than €2m and the creditors, including Revenue, would get very little, however if the company was to continue as a going concern that deficit would be reduced to €390,000.
Previously the court heard that its problems arose mainly from a decision of the directors Paul Byrne and Fiona McHugh to concentrate on front of house duties, while leaving financial administration to an under-qualified book keeper member of Mr Byrne's family.
Between 2006 and 2009, and unbeknownst to the directors, substantial arrears of taxes in the region of €840,000 had been allowed to build up, despite relevant returns having been made to the Revenue Commissioners, which eventually issued letters of demand and ultimately a petition to wind up the company.
The court was told more than €200,000 was also misappropriated from the company.
