Your friend will receive: [Friend] has invited you to join them in Fallen London, where they have entered their pet weasel in a tournament. They need you there for moral support. And the bookies are offering good odds on their weasel... Join them now!
[Friend] has joined you in Fallen London! And you've won a little something at the weasel-fights.
Twitter/facebook message is: [Friend] invites you to join them at a tournament of Weasels! They know your presence will bring them luck!
In messages, the invitation is refered to as "An Invitation to a Weasel-tournament"