I keep forgetting to suggest this, but when one accepts a game invitation and writes a message to the inviting player, that message never reaches the invitee! (or nobody has ever replied to my invitations with a message!). My suggestion would then be that if one replies with a message to an invitation, either the invitee gets also a message saying "your invitation was accepted with the following message..." or that that message is automatically added to the history of messages of the current game (like a message on move zero :-) )