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It should be something like this (one on top, other on bottom (something about 180 degree) (for both, for sphere and scene environment (world))

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Basically it comes down to this, you need slightly different settings for Object and World. I'm sorry but I have no HDRI where the horizon is in the center or slightly below the image, so in my example you will still see some landscape - but the setup works. Maybe you have a better HDRI.

For both Object and World you use Generated coordinates. For the sphere this means, the projection method in the Image Texture node has to be set to Sphere instead of the default Flat. The Environment Texture for the background can use the default Equirectangular.

Then you need a Vector Rotate node to rotate the coordinates for one of the textures. For both the Axis should be (1, 0, 0) and the Angle 180°. However the Center needs to be (0.5, 0.5, 0.5) for the sphere but for the world (0, 0, 0). If you wonder why I don't use the Mapping node for rotating the vectors by setting Scale Z = -1, this works for the world, but not the sphere, so I simply used Vector Rotate on both.

Next is a Separate XYZ node from which the Z output is plugged into a Color Ramp. This is to make the transition between the original and the rotated texture. For the Object, black and white should be around the center (0.5) of the color range, while the World needs them on the left side towards 0.

The original and the rotated coordinates each go into the Vector input of two texture nodes, both with the same image (although you could of course mix two different images as well). Their output goes into a Mix Color node, the rotated at the top and the original at the bottom. The mix factor is the Color Ramp output.

mixing flipped textures

And the result is this - as I said, unfortunately I had no HDRI where the horizon is low enough. Of course you could use a Mapping node to transform the texture up and down, but then you will have the same problem with stretching and distortion like mentioned in my answer to your other question.

resulting sphere and sky

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