Here is the only letter of R' Moshe Feinstein in the LBI Bloch Archive. RMF is sending Bloch 5 dollars for his book מי נתן and thanking him for reminding his wife because RMF is busy and had forgotten.
Bloch claims to have had more extensive correspondence with R' Moshe in his pamphlet והיה מחניך קדוש against R' Moshe's p'sak on artificial insemination (See also Igros Moshe EH 2:11). Bloch asked R' Moshe if he permitted him to publish this pamphlet against him. R' Moshe's response is a classic and well worth reading. I hope to scan and place online next time I have access to the pamphlet..