First, the fog image must be continuous. His end is to amend the beginning to transmit an infinite continuity.
The information below take into account that your game has the resolution of 800x600 and the fog image size is 800x600.
On start of layout
FOG - Set size to (LayoutWidth+1600, 600)
FOG - Set position to (0,0)
System Every tick - FOG - Set X to Fog.X-(dt*120) (or put a value that you think more apropriate)
FOG X <= -800 - Set X to 0