There could be a couple of reasons for that. In the UV/Image editor select all the face then in the Header menu select "UVs >> Scripts >> Save UV Face Layout", that will save a proper UV texture map rather than just using a screencapture (which is what you appear to be doing?).
Also when you export to OBJ make sure to "Apply Rot/Scale" (Ctrl+A), if you export the object from Blender without doing that it will revert to the position is *was* in before the mesh was moved, rotated and so on. You're not having done this may account for the misalignment.
You'll also need to check that the converter isn't switching axis and flipping things around.
