I have experimented with things on and off for this. And I haven't yet found something that has stuck that I have really liked.
I have done photos of letters sent (though that was often in response to letters being lost (sending to Italy and Turkey went through an unreliable patch) I really do need to go through those files and remove them from using themselves as screensavers on the computer!
I have a letter log (date in and out) - so far I am maintaining that quite well - it just is a page in my journal and keeps that to hand.
I have tried a brief summary of the letter posted and received and never managed to be diligent in keeping it up - but was tempted to play around with it in the intensity of Incowrimo as it is so easy to forget what I have said to who.
And, finally, when I am writing or receiving a significant - relationship altering type letter- I tend to transcribe that into my journal so I do not lose the nuance of what has been said. I also put relevant texts or emails quoted in at such times. Needless to say, that is not a regular occurrence.
So I'd say experiment and see what works for you. Don't be worried about sticking to something in it's first format, wiggle it until it works for you.