After completing Polite Society, Valentine Style, head to the sheriff’s office in Valentine to trigger this mission. After the cutscene, the last known location of the target will be marked in the map. Mount your horse and ride to the location.
The target has set up camp in the rocky trail beside the river. You don’t need to sneak in to capture him; approach the target and confront him to trigger a cutscene. During the cutscene, Benedict will slip but Arthur will grab him in time. Try to pull him up but alas, he’ll still fall down the river.
The current will carry him so ride your horse and ride fast to catch up. Prepare your lasso and get close enough so you can catch him. Pull him out of the water then keep holding L2 as you approach to keep him lassoed. When you’re standing beside him, hogtie him and stow him at the back of your horse. You’ll have to deliver this man back to the sheriff in Valentine.
While riding back to town, you can keep hitting the bounty to silence him. After reaching the sheriff, hit your horse then carry him inside then drop him to the holding cell. You’ll receive your money and mission complete.