So sorry for your pain FOOH.
Yes you should tell his wife, but not to prove anything or to get revenge. You should tell her because she deserves to know and to make choices for her own life. Would YOU want her to tell you, if she knew about her H and your W, and you did not?
Tell her gently, and offer proof. She will be hurting, and she is not at fault here.
Crazy how the W mind works. My WH too was "just friends" with his coworker whom he talked to hundreds of times a month at all hours and spent 14 hrs a day with and 1000s of dollars on. Interestingly though, he thought he should keep that relationship a secret - from his mistress!