You can’t. The background object isn’t visible in refractions. Or reflections, or anything but camera rays.
Here’s an example: a refractive sphere in front of a torus, in front of the background checkerboard object. The black areas are where the background object isn’t visible to refraction rays.
The “background object” is actually a shader plugged into the Arnold background slot.
You won’t see it in Cinema 4D, but when C4DtoA translates the scene to Arnold, the background object is translated as a shader plugged into the options.background parameter (in Cinema 4D, this is the Environment > Background parameter in the Render Settings).
In an ASS file, it looks like this:
options { background "c4d|Background" } image_plane { name c4d|Background color c4d|Arnold_Shader_Network|checkerboard lenx 1 leny 1 ox 0 oy 0 }
The image_plane node is a shader, and if you were to check its code, you’d see that it handles camera rays only; for any other ray type (like refraction), the image_plane shader returns black.
shader_evaluate { if (!(sg->Rt & AI_RAY_CAMERA)) { sg->out.RGBA = AI_RGBA_BLACK; return; }