Read the history. Szilard wrote that letter. Einstein tweaked it a little with Szilard, at most. Szilard was taking it to Roosevelt and for obvious reasons did not want his signature on it, so Roosevelt wouldn't dismiss him and the letter as from an unimportant scientist with a self-interest in his own patent.
We are very close on this. I wish you well. NRN (no response necessary). We have neither Szilard nor Einstein to resolve this perfectly. Both would have, fortunately for us, told us the truth if asked.