You have to be playing the True Pacifist Route up until the very end. Then, when you defeat Flowee without killing it, it sends you back to the start screen. Reload your save, but be aware the internal game has saved the fact you fought Flowee and are reloading. I don't know how it does that, but anyway, don't fight Asgore this time. Go through the throne room, through New Home, and the CORE back to the MTT resort. You'll get a phone call from Undyne to meet her in Snowdin and go and do that. There's the letter.