Jérémy,
For invitations, no, you can't let the user set a message. That's how Facebook works with their invitation. They let you (the administrator) set the title, message and URL to send the user to.
If you want to let users share content with their friends, that is something we can help you with. It won't be an invitation to the site, but would share specific pages from your site.
If you have any questions, let me know.
Thanks,
Alex