Are you suggesting that the correct constructions would be "write to me a letter or fax to me the results"

Darling Fishie, dinna make it harder than it has to be! the "correct" constructions, if they include "to," would read/speak thusly:

write a letter to me
fax the results to me

They get bollixed around when people leave out the "to" - so perhaps both forms are correct.

Jackie, how nice to see you here again! What you said, above, reminded me of another elision: back in high school, a group of us were deciding where to go for lunch, I think it was - someone must've said, "McDonald's," because I said, "Don't let's," and someone else said, to me, "Don't say, 'Don't let's'! It's wrong!" Now, I had heard "don't let's" used by my (British) parents, who were quite well-educated, so I believed I was correct, but I was less assertive in them days....The teacher who overheard us leaped in, though, and said, "There's nothing wrong with 'Don't let's' - it's a contraction of 'Do not let us'."

So I guess, a story about contraction, rather than elision....

Let us go in peace to love and serve the board.