Answer:
Join.
Explanation:
The word "braid" is, originally, used to describe the act of lacing or weaving things together such as hair or yarn. It is the interlacing act that is typically known as a braid.
In the given sentence, the speaker uses this word to talk about how "immigrants braid their past into American story", implying how immigrants' stories are included in American stories. And the best word to replace or, the word that means the closest to "braid" is "join", as they both imply the 'inclusion, the fusion' of two elements.
Thus, the word "join" will best replace the word "braid" in the given sentence.
