Elizabeth would not have been able to convey her feelings in any other way. The two were far apart, communication was limited to letter writing. In the letter, Elizabeth basically invites Frankenstein to back out of their marriage plans, something he only considers because of the monster's threats. The letter, however, only serves to make Victor's commitment stronger, and he decides that it is time to marry Elizabeth rather than walk away.
But it is your happiness I desire as well as my own when I declare to you that our marriage would render me eternally miserable unless it were the dictate of your own free choice.
This letter revived in my memory what I had before forgotten, the threat of the fiend--"I WILL BE WITH YOU ON YOUR WEDDING-NIGHT!" Such was my sentence, and on that night would the daemon employ every art to destroy me and tear me from the glimpse of happiness which promised partly to console my sufferings.
I resolved, therefore, that if my immediate union with my cousin would conduce either to hers or my father's happiness, my adversary's designs against my life should not retard it a single hour.