JFBConnect doesn't have specific integration for AcyMailer, but we know of many users who have both JFBConnect and Acy working on their sites without any issue.
JFBConnect uses the standard User plugin system, which lets 3rd party extensions 'do' something when a new user registers or logs in. For JFBConnect, with our automatic registration mode, AcyMailer can automatically add a user to the newsletter list. If you use our form-based registration mode, if AcyMailer is simply extending the standard Joomla registration form, then those fields should show on our registration page as well.
You shouldn't run into many issues with combining our extensions, but if you do, just let us know and we'll help however we can.
Thanks,
Alex
Integration with AcyMailer
