In order to move/rotate/scale the result of a baked soft body or cloth simulation you can export the data to a suitable format and either Import it (into a set of shape keys) or use the exported point data to drive a Mesh Cache modifier. This can be achieved via the MDD Importer/Exporter which is available as an addon (User Preferences/Add-ons).
For the 'shape key' method, simply select your bakes soft body/cloth mesh and select File/Export/Lightwave Point Cache(.mdd) from the menu. This allows you to create an MDD file containing the data from each of the vertices in your mesh.
Now select File/Import/Lightwave Point Cache(.mdd) to re-import the point data and the add-on will automatically generate animated keyframes to animate your object between frames. At this point you can remove the Soft Body physics as the animation will be purely keyed.
You can now move/rotate/scale your mesh and the animation will still be applied.
See https://blender.stackexchange.com/a/106400/29586 for a further example of this.
Mesh Cache Modifier
Another option is to access the exported MDD data via a Mesh Cache Modifier. The modifier reads the exported MDD data and applies it directly to the mesh. This has the advantage of avoiding the complexity of keyframed shape keys and allows the animation to be more easily 'tuned'.
This can produce the following result :
Here the centre cloth falling on the cube is the original simulation. The point cache has been exported to an MDD file and the mesh duplicated (without the simulation) and Mesh Cache modifiers used to re-apply the simulation on each of the copies - at different start frames and orientations.
A further example of this can be found here https://blender.stackexchange.com/a/10661/29586