This is a difficult and challenging problem, this common hepatic duct stone should be removed, ERCP can be done in patients with Billroth II gastrectomy, but it is technically demanding, if this can be done a wide papillotomy and dormia extraction of the stone can be performed. I know that it was difficult for you during open exploration of CBD to dislodge this stone, but it worth trial with the strong Olympus dormia baskets to engage the stone and extract it, if it was difficult to extract you can crush it with lithotripter. If you failed to engage the stone in the dormia then you can insert a nasobiliary tube to be used to locate the stone, by injecting dye into CBD, during extracorporeal shock wave lithotripsy.
If it was difficult to locate the papilla during ERCP, a percutaneous transehepatic route can be established and a guide wire can be passed percutaneously, by-passing the stone, to the duodenum where it can be retrieved by the scope and a papillotomy knife passed over the guide wire to do papillotomy and attempt the above steps.
If the guide wire could not pass the stone percutaneously, you can insert a drainage tube to be used for drainage of biliary tree and to locate the stone during extracorporeal shock wave lithotripsy, if this was successful, then you can pass a guide wire to the duodenum, use it for papillotomy to clear the biliary tree from stone fragments.
If all of the above failed, you will have two choices:
1- Leave the patient to his fate of recurrent attacks of cholangitis which will be fatal sooner or later.
2- Re-explore the patient, try to extract this stone by direct incision on it in the CHD, and the last option left is a hepaticojujenostomy.