Phyrexian metamorph question

[Hamstar]

If I cast {phyrexian metamorPh} as a copy of {Chandra's Phoenix} and it dies, does it reside in the graveyard as {Chandra's phoenIx} and come back when I deal damage to my opponent with {red sun's zenith}? Could he make a different copy if/when he comes back?

[BlackJester]

Once it leaves the BF, even briefly with {Cloudshift}, it stops being a copy.