We only got told over the phone too but I'm sure they would give us something in writing if we asked. We will be asking for something if we move to another clinic because we will absolutely need to show what happened to another FS.
You're right though, they really should put something in writing!
I wonder why on earth they are sending you a letter! Maybe your DP is right and there is another embryo that they forgot to tell you about? Or it could that they stuffed up there papers and they just think you have another. Let us know how you go in the morning! I'm sure it will be easily sorted 😊