Export surface from one model to another

You will have to make it its own body. If it is not a single body, you can use the "Offset Surface" command to make a copy of it, just set the offset distance to zero. Once you have the surface copied, find the surface body in the Feature Manager Tree, in the surfacing folder. Right click on it, and select "insert into new part..." You can then export and save that surface.

Select a face and do a Save As --> Parasolid. You will be asked if you want to export only selected faces selected bodies, or all bodies.