[Fluxx] Radioactive Potato timing question

[Timothy Hunt]

You can't win, if the Radioactive potato is in front of you.

So, let us say the play order is

Andy -> Becky -> Charlie

Andy has Love (and no other Keepers).  Becky has Radioactive Potato

If Charlie plays "All you need is Love", does Andy win immediately?
or does the RP move to Andy before he can win, and thus temporarily
prevent him from winning until he can get rid of it (perhaps by
playing Double Agenda and another goal)?

(Note that the opposite situation is clearer - if Andy has Love and
RP, then when AYNIL is played, RP moves on, and Andy then wins)

Timothy