Is there a way to parent or constrain Baked particles to an object?

I bake a particle simulation, it works fine I can scrub the timeline and I see it’s baked. When I move the Emitter after that though, the particles don’t follow.
I would like to be able to animate the emitter (translate+rotate) and have the baked particle animation just follow as if it were a keyframed animation itself.
In other words, the particles would behave like children of the emitter as it moves.
I don’t care it it needs to be constrained or parented or what not, i just am looking for a way to make that happen.
Any help would be greatly appreciated !