In reply to David Alcock:
If that made you cry you are not alone. I found this quote on the Wikipedia page for the quartet:
"The Borodin Quartet played this work to the composer at his Moscow home, hoping for his criticisms. But Shostakovich, overwhelmed by this beautiful realisation of his most personal feelings, buried his head in his hands and wept. When they had finished playing, the four musicians quietly packed up their instruments and stole out of the room."
As you probably know the second movement is derived from the Dance of Death movement of the second Piano Trio, which is believed, I think, to represent the dance Jewish concentration camp prisoners were made to do on the edge of their mass grave shortly before being shot.
The ever-fascinating life story of Shostakovich, so intimately related to his music, is well described in this article:
https://robertgreenbergmusic.com/the-string-quartet-in-time-of-war-dmitri-s....