Copper layer doesn't stick after Copper electroplating
Roughen the deposition surface, perhaps by buffing with very coarse sandpaper or an abrasive scrub pad or similar.

If the surface isn't rough enough, the deposited coating has nothing to mechanically "grab onto" and it can be peeled off just as you've observed.  With a sufficiently rough surface, the deposition penetrates into the nooks and crannies of the surface texture and adheres very strongly.