Is there time to do that? I'm assuming it gets done in the moribund state.

No. You cannot. Moving Poisoned Wine is an "Any Phase" action. You will only ever be able to use Response effects between a creature being killed and that creatures (and its attachments) leaving the table.

And even if you could hypothetically move it in the moribund state, moving it would not take it out of the moribund state. It would still leave play - even off of a new creature - when the original killed creature left play.

Thanks, ktom.

Last time I've had simmilar problem. I played against Targaryen and got Poisoned Wine on my 3 STR character. It's STR was lowered to 1 and on next plot phase Targaryen player played Threat from the North plot card and killed my character. Q: Can Targaryen player use the ability of PW?

You said "killed," but meant "discarded," right?

You cannot move Poison Wine off of this character for the exact same reasons cited above. The timing is wrong for the "Any Phase" effect.