you cannot modify the position of something in the pixel shader, that can only be done before, in the vertex shader.
So in your case you would need to add something like this:
VertexShader = compile vs_5_0 VertexShaderFunction();
PixelShader = compile ps_5_0 BackgroundShift();
The pixel shader can only work on a pixel with a set position.
However, what you can do in the pixel shader is to read the pixels of an image but with an offset to the left for example, this would look like a texture shift.
An example would be
float4 PixelshaderFunc(float4 pos : SV_POSITION, float2 texCoord : TEXCOORD0) : SV_TARGET0
float4 pixelShift = ScreenTexture.Sample(LinearSampler, texCoord.xy + float2(0.1f, 0.0f));