Can I shim the top of an 6x6 post that is supporting a beam?
If I was making a shim, I would not want the grain running the short way since it will tend to disintegrate under load and time.   Ideally 7/8 plywood, partly because it is harder wood... otherwise plane or rip 2x6 or two 2x4s to the desired thickness, or 1x6 if the thickness will suffice.  I would also glue and screw it.