Q: If a Creeper is moved from one player to another, does the receiving player get to “immediately re-draw” as it says on the card?

A: The “Immediately redraw” is only for if that person has DRAWN a Creeper (or was dealt one at the beginning of the game). The idea is that, if you’re drawing, you are drawing to get a non-Creeper. If you get a Creeper, you are required to play it immediately, and because that draw-play acquisition was involuntary, it doesn’t count as a play or a draw for you… so you get to try again for a NON-Creeper. If you’re just taking or receiving a Creeper that was already in play somewhere else, you’re not attempting to execute a draw, you just get the Creeper.

Another way to note this is the case is that is says REdraw. If you didn’t get the Creeper by Drawing, then you can’t REdraw.