Yes, the Lend-a-Hand Extra Large Folding Grab Handle for RVs # AM-533 that you referenced will fit your 2015 Forest River Cherokee 16BHS. The mounting bracket dimensions will be the same as what you have since this was designed to be as universal as possible and fit that standard bracket dimensions on RVs that is 19-1/4 inches apart. The extra dip in the handle will also be easier for kids to reach.
I attached a review video for this for you to check out as well. view full answer...