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A technique for the design of conformal metasurfaces with two spatially disconnected space wave ports connected by a surface wave is presented. The passive and lossless metasurface absorbs the incident wave at port 1, converts it nearly perfectly into a surface wave which transports the energy along an arbitrarily shaped/curved metasurface to port 2, then reradiates the captured power as a radiated field with control over its amplitude and phase. Since the incident field is seen to disappear at the input port and reappear at a spatially dislocated port as a new formed beam, the space wave can be said to have been seamlessly transported from one point in space to another. The metasurface consists of a single, conformal, spatially variant, impedance sheet supported by a conformal grounded dielectric substrate of the same shape. It is modeled using integral equations. The integral equations are solved using the method of moments (MoM). The impedances of the sheet are optimized using the adjoint variable method to achieve the near perfect wave transportation operation from a passive and lossless metasurface. MATLAB codes and COMSOL Multiphysics simulation files for all designs presented in this paper are available for download as supplemental material files. Possible applications include channel optimization for cellular networks, inexpensive power harvesting, sensing, around-the-corner radar, and cloaking.