The investigators propose to replace HLA- partially compatible allogeneic Hematopoietic Stem Cell Transplantation (HSCT) for FHL type 3 patients, with autologous transplantation of immunoselected gene-modified CD34+ cells, combined with transduced autologous T-cell each time this is possible and also to propose this alternative treatment as salvage in case of failure of a previous allogeneic HSCT. This approach should avoid the severe immunological complications (failure to engraft, acute or chronic graft versus host disease (GVHD)) and conditioning toxicities such as severe Veno-Occlusive Disease (VOD). As the clinical manifestations of FHL type 3 patients are triggered by opportunistic viral infections (often EBV) and can be poorly controlled or only transiently controlled by the available drugs , providing the patient after the conditioning with immediately functional autologous cytotoxic T-cells could be key to maintain the control of the viral infection and hopefully its eradication awaiting for the hematopoietic reconstitution . This procedure should avoid any reactivation of the viral infection and thus improving the patients' overall survival and event-free survival while clearing the ongoing triggering infections.