The question asks about the author of the partition narrative titled "The Other Side of Silence".

Option 1, Amrita Pritam, is an incorrect choice. She was a prominent Punjabi poet and novelist, known for her work "Pinjar", which is also centered on partition but not the book we are searching for.

Option 2, Urvashi Butalia, is the correct author of "The Other Side of Silence". She is an Indian feminist writer and publisher, who has contributed significantly to the field of women’s studies in India. Her narratives in this book are based on the ‘silenced’ voices from the time of the India-Pakistan partition.

Option 3, Saadat Hasan Manto, is not the correct author. He is famous for his short stories, particularly those revolving around the partition, such as "Toba Tek Singh" but did not write the book in question.

Option 4, Manju Kapur, is a renowned Indian novelist best known for her book "Difficult Daughters" which depicted a partition story but she is not linked to "The Other Side of Silence".

Hence, Urvashi Butalia is the correct author of the book "The Other Side of Silence".