"Dear Ben & Jimmy," the accompanying note read. "Here's my fax. Love, MD. Faxtag: KimmelHasManBoobs."
The trio's online joke war started last week, when Affleck took to Twitter to promote a charity contest benefiting Eastern Congo Initiative and Water.org. The contest gives two lucky fans a chance to hang out with the Argo director and BFF Damon in Hollywood.
"@JimmyKimmel -- I thank you buddy," Affleck tweeted after Kimmel voiced his support for the charity effort. "And @easterncongo & @water thank you! Matt, on the other hand? Matt, you there? Right. We will fax you."
Kimmel, 46, then added his own jab at the Twitterless Damon. "Matt is probably too scared to get on Twitter because no one likes him," he joked.
Added Twitter CEO Dick Costolo: "@BenAffleck, @JimmyKimmel, @water, we have printed out this tweet and placed it in a suitcase that we will have couriered over to Matt."