Grading with sig and a cert

Got an invincible #1 foil signed by lipwei chang. Included is a certificate of auth. Yeah i know it can mean nothing or everything. If i send this in to cgc for sig authentication and grading should i send the certificate showing the possibility of the sig being real or keep the cert at home and just let them authenticate the sig their own way?
Im sure if i include there is always the possibility of it getting lost or trashed by someone who thinks certificates are useless. Am just wondering if the sig is authentic is there a way to include the cert in the slab? I know the yellow label will indicate authenticity but i like to keep things together. Otherwise its plan B and put the cert in a bag and tape it to slab.