so, the only viable method I found, if for you to follow this tutorial, and transfer the Dynamics to a hierarchy of objects, after you bake the mograph Cloner to a mograph Cache tag.
https://lesterbanks.com/2015/03/bake-mograph-animations-to-objects-using-xpresso/
After you have successfully transferred the Dynamics to the Objects, hide the Cloner, go to the last frame, apply your material to the Parent Null using a Flat Projection, and when you're happy, from the Tags menu, do a "Copy Tag to children"
This will apply the material at THAT frame, at THAT position for all tiles. When you scrub back, you'll see that the texture is stuck on each tile.
I have used another method to make the activation of the Dynamics similar to the original emitter.
Project link attached:
https://www.dropbox.com/s/pn6n8ow1cuqrwsl/Tiles 01A.c4d?dl=0