After the parallel motion of the strings in C-sharp minor near the end of the second movement, the music played by the
first violin becomes free rises, and soars, and the music is in A-flat Major. That, my friends, represents the triumph and elevation of the human soul over pain, suffering, and bleakness where there seems to be no hope. Beethoven was deaf when he composed this string quartet.
I recommend listening to the LaSalle Quartet play the second movement from 6:16 to 20:52 in the YouTube video.