How to send message using Organic Groups Invite?
Not sure if it is an option you're willing to consider, but the OG Invite People module might be used as a possible alternative for send such invitation to a group. Here is a quote from its project page:

... adds the missing email invite functionality for OG 7.x-2.x.
When you click on &quot;Invite user&quot; a user is created and invited to the group right after. No registration process is needed. Invitee receives an email with one-time login link.