Quantum mechanics forbids that much knowledge. If you take the present state and apply the advanced Green function to it, you don't end up with one distinct letter written. Similarly, if you take a future state where you wrote one particular set of letters and apply the retarded Green function to it, you don't get the present state. So she isn't your girlfriend yet... but she will be once you write or receive your last letter from her.
I just realized I haven't previously pointed the metaphysicians on Less Wrong to "Possible Girls," a hilarious paper about acausal romance:
Even if you don't read the whole thing, don't miss the final paragraph.