An allogeneic cultured postnatal thymus tissue-derived product for use in a method for inducing thymopoiesis and promoting donor-specific tolerance to an allogeneic solid organ transplant obtained from a deceased donor, in a recipient in need of a solid organ transplant, wherein the allogeneic cultured postnatal thymus tissue-derived product is prepared by subjecting suitable thymus tissue, which has been obtained from the donor, to a conditioning regimen for a period up to 21 days to produce the allogeneic cultured postnatal thymus tissue-derived product; wherein the conditioning regimen for the donor thymus tissue comprises aseptically processing the donor thymus tissue in a thymus organ medium to produce partially T-cell depleted donor thymus tissue slices; wherein the partially T-cell depleted donor thymus tissue slices show areas positive for cytokeratin (using antibody AE1/AE3) scattered throughout the tissue, the presence of at least one Hassall body, CK14 staining scattered throughout the tissue and presence of intact nuclei; wherein the method comprises the steps of: (a) removal of the thymus of the recipient; (b) treating the recipient with an induction immunosuppressive regimen comprising one or more immunosuppressive agent to deplete the recipient's T cells and/or to suppress the recipient's T cells from rejecting the transplanted solid organ; (c) providing both a suitable solid human organ and a thymus gland from a deceased donor; (d) transplanting the solid human organ into the recipient; (e) treating the recipient with a maintenance immunosuppressive regimen; and (f) implanting the allogeneic cultured postnatal thymus tissue-derived product into the recipient after 12 to 21 days of conditioning regimen, wherein the dosage of thymus tissue slices is about 1,000 - 20,000 mm 2 of thymus tissue surface area/ recipient body surface area in m 2. wherein the allogeneic cultured postnatal thymus tissue-derived product is prepared by subjecting suitable thymus tissue, which has been obtained from the donor, to a conditioning regimen for a period up to 21 days to produce the allogeneic cultured postnatal thymus tissue-derived product; wherein the conditioning regimen for the donor thymus tissue comprises aseptically processing the donor thymus tissue in a thymus organ medium to produce partially T-cell depleted donor thymus tissue slices; wherein the partially T-cell depleted donor thymus tissue slices show areas positive for cytokeratin (using antibody AE1/AE3) scattered throughout the tissue, the presence of at least one Hassall body, CK14 staining scattered throughout the tissue and presence of intact nuclei; wherein the method comprises the steps of: (a) removal of the thymus of the recipient; (b) treating the recipient with an induction immunosuppressive regimen comprising one or more immunosuppressive agent to deplete the recipient's T cells and/or to suppress the recipient's T cells from rejecting the transplanted solid organ; (c) providing both a suitable solid human organ and a thymus gland from a deceased donor; (d) transplanting the solid human organ into the recipient; (e) treating the recipient with a maintenance immunosuppressive regimen; and (f) implanting the allogeneic cultured postnatal thymus tissue-derived product into the recipient after 12 to 21 days of conditioning regimen, wherein the dosage of thymus tissue slices is about 1,000 - 20,000 mm 2 of thymus tissue surface area/ recipient body surface area in m 2. (a) removal of the thymus of the recipient; (b) treating the recipient with an induction immunosuppressive regimen comprising one or more immunosuppressive agent to deplete the recipient's T cells and/or to suppress the recipient's T cells from rejecting the transplanted solid organ; (c) providing both a suitable solid human organ and a thymus gland from a deceased donor; (d) transplanting the solid human organ into the recipient; (e) treating the recipient with a maintenance immunosuppressive regimen; and (f) implanting the allogeneic cultured postnatal thymus tissue-derived product into the recipient after 12 to 21 days of conditioning regimen, wherein the dosage of thymus tissue slices is about 1,000 - 20,000 mm 2 of thymus tissue surface area/ recipient body surface area in m 2.