A someone who posts regularly in the Customer Support forums, I’m going to recommend against their suggestion.
Keep them on ignore. Ignore will ignore all their characters on that account, but only for the character you’re logged into. If you have multiple characters, put them on ignore on each of them.
Praetorian is correct. If you don’t have them on ignore and you reply to them in any way whatsoever, it’s no longer harassment. It’s a conversation and Blizz will not take action. You must keep them on ignore.
If this player logs into another account to message you, even once, you’ll want to open a ticket for Ongoing Harassment and do that for every attempt they make to bypass ignore.
Have a good read over the CS thread Spotlight On: Harassment. It’s a good read for a situation like this.
Also, there is absolutely no need to “document” or “screenshot” anything really. You’re welcome to for your own records, but Blizz already has all of the logs in-game. They don’t need a screenshot to see what’s being reported 
If you have any other questions, feel free to pop on over to the CS forums.