Berrygerry beat me to it!
I was gonna emphasize the same point. Elders are strongly admonished to never approach sisters alone. You could extend that to text messaging. Hell--they do! According to them, simply texting members of the opposite sex is considered "dating" (this is even on the 'About Us' section on JW dot bOrg!).
Either this guy is an over zealous newbie who doesn't quite get the elder protocol yet, or he really is trying to chum up to her. It would be entirely different if he had his wife text your wife, but this isn't what's happening. I wonder what HIS wife thinks--or if she even knows.
If I were in your situation, I'd contact 2 other elders on the body and explain that A) he's not following procedure for elders, B) it makes you very uncomfortable and C) this guy is opening himself AND the congregation up to severe liability. Explain to them that you're not accusing anyone of having bad motives, but, there are a lot of jealous, insecure, over-protective hothead husbands & loopy "Potipher's Wives" out there (JW or not) who could easily misunderstand things & make a really nasty, publicized & embarrassing mess over something like this.