A lymph conduction system implant (10) includes a stent graft (12) and a porous membrane (14). The stent graft has a non-porous tubular side wall (16) with a proximal end (18) and a distal end (20). The non-porous tubular side wall is configured to define a lumen having an inflow port (24) at the proximal end (18) and an outflow port (26) at the distal end (20). All exposed surfaces of the stent graft are made of a first biocompatible material. The porous membrane (14) is connected to the proximal end of the non-porous tubular side wall of the stent graft and is configured to span an entirety of a transverse area of the inflow port of the lumen of the stent graft. The porous membrane is made of a second biocompatible material. In a preferred embodiment the porous membrane (14) is configured as a drug eluting porous membrane that carries a drug.