A percutaneously implantable replacement heart valve, which valve comprises: an outermost envelope portion of shape-memory material, a collapsible-expandable heart valve stent of generally tubular shape; and a valvular device comprising a plurality of flexible leaflets disposed interior of said stent, which leaflets open to permit blood flow in a downstream direction and close to prevent blood flow in an upstream direction therethrough, characterized in that the collapsible-expandable heart valve stent includes proximal and distal rings (33, 73, 31, 71) and at least three spaced apart posts (35, 69) that extend axially between said rings, and the outermost envelope portion comprises a plurality of spaced apart distally and proximally extending arms (17, 75, 19, 77) of shape-memory material having free ends, said distally extending arms (17, 75) being constructed to wrap around the native leaflets by bending back toward said proximally extending arms and contacting downstream-facing surfaces of the native leaflets and said proximally extending arms (19, 77) being constructed to swing radially outward at their free ends toward said bent-back distal arms and contact upstream-facing surfaces of the native leaflets, so as to sandwich the native leaflets of a stenotic valve between said two sets of arms, wherein a tab, which is apertured to form a circle or eyelet, is formed integrally with the free end of each arm to serve as eyelets through which a control string arrangement is removably connectable to facilitate the installation of the outermost envelope portion within the orifice of the native valve which the replacement heart valve is to replace. an outermost envelope portion of shape-memory material, a collapsible-expandable heart valve stent of generally tubular shape; and a valvular device comprising a plurality of flexible leaflets disposed interior of said stent, which leaflets open to permit blood flow in a downstream direction and close to prevent blood flow in an upstream direction therethrough, characterized in that the collapsible-expandable heart valve stent includes proximal and distal rings (33, 73, 31, 71) and at least three spaced apart posts (35, 69) that extend axially between said rings, and the outermost envelope portion comprises a plurality of spaced apart distally and proximally extending arms (17, 75, 19, 77) of shape-memory material having free ends, said distally extending arms (17, 75) being constructed to wrap around the native leaflets by bending back toward said proximally extending arms and contacting downstream-facing surfaces of the native leaflets and said proximally extending arms (19, 77) being constructed to swing radially outward at their free ends toward said bent-back distal arms and contact upstream-facing surfaces of the native leaflets, so as to sandwich the native leaflets of a stenotic valve between said two sets of arms, wherein a tab, which is apertured to form a circle or eyelet, is formed integrally with the free end of each arm to serve as eyelets through which a control string arrangement is removably connectable to facilitate the installation of the outermost envelope portion within the orifice of the native valve which the replacement heart valve is to replace.