Some years ago, there was a rather silly movie made about Beethoven entitled Immortal Beloved. It was based on the descriptor that Beethoven used in three letters to an unnamed woman. Many scholars now believe that Beethoven's Immortal Beloved was Antonie Bretano, a woman he met in 1812 at the Czech resort of Teplitz (you can read more about it here).
The letters he wrote have a desperate yet poignant quality to them. They hint at a deep love, a recognition at the soul level, yet acknowledge that their desire to be together could not happen. Whether they were true Twin Souls or not, I do not know, but I believe that this deep soul recognition is expressed in the phrases that he uses: "Ah, wherever I am, there you are also," and "Is not our love truly a heavenly structure, and also as firm as the vault of heaven?"
Even if Beethoven and Antonie weren't true Twin Souls, his calling her his Immortal Beloved hints at his recognition that there exists a love which overcomes difficult circumstances, distance, and even time. I would like to think that his knowing about his Other Self -- his Twin Soul -- caused him to feel understood and safe enough to dig deep inside himself to create his extraordinary music.