The first letter that Victor receives from his cousin, Elizabeth, is in Chapter Six, and is delivered to Victor by Clerval at a time when Victorsuffering from devoting himself to his work and study to his branch of arcane scientific knowledge. As he reads Elizabeth's letter, and hears of her concern about him because of the lack of news he has sent them, it is clear that the receiving of this letter marks the beginning of Victor's improvement in terms of his personal health. Note what the text tells us his response to reading her letter was:
"Dear, dear Elizabeth!" I exclaimed, when I had read her letter, "I will write instantly, and relieve them from the anxiety that they must feel." I wrote, and this exertion greatly fatigued me; but my convalescence had commenced, and proceeded regularly. In another fortnight, I was able to leave the chamber.
Thus we can see that the letter Victor receives from Elizabeth has the impact of restoring Victor to a state of health and sanity, reminding him of the love that others have for him and what is important to him, acting as a much needed correction to his single-minded and obsessional focus on the pursuit of scientific knowledge.