Thanks for the answer - Just the tool I was looking for. The lower left corner of my grid is now in the right position - But the CellSize is not taken over, so my moved grid is too big.
"in_snap_raster" is set to the original grid - Did I miss anything here?
Edit:
Documentation says
"The cell size of the output raster will be the same as that of the input raster."
My InputRaster's cell size is ~0.48
My OutputRaster's cell size is 1.