There is no proper explanation given by the episode except that ''it will have to remain a mystery'' as said by Beckett. But there can be only 2 sources of the letter:
1) Vivien- It proves that she indeed was a psychic medium and was able to predict her death though quite ambigiously.
2) Paula- As claimed by Beckett, Paula could have done this in the stipulated time, though it is quite difficult considering the timeline i.e. she was back at the restaurant by the time Nick was still pounding at the door.
So, it is quite unclear.