Not sure if I understand your statement about the error.  Where are these email addresses that you compared and which are supposed to be different?

Normally, even if the email address you try to send an invite to is different from what was registered previously, the system will only prompt you to confirm whether it's the existing or new email address you'd like to use rather than stopping you in the track.

Can you post a redacted screenshot or copy and paste the exact error messages you're getting in both Lacerte and Intuit Link?