Max Login Reached.

Normally, you'd contact the FM folks - see https://helpx.adobe.com/contact/enterprise-support.other.html#framemaker for your Adobe Support options. I'd recommend using the tcssup@adobe.com e-mail address as it reaches a team dedicated to Technical Communication Suite products including FrameMaker.
But in this case, you can probably follow their advice like this:

Greetings from Adobe! Could you try the following steps:-

• Login to:- https://account.adobe.com/activated-devices
• Use the same ID where the product is registered.
• On the manage account page click on Plans & Payment and click on Activated Devices.
• On the next window, it will show you options to deactivate the devices.

In case the issue persists,  close all Adobe applications and try the following steps.

• Go to the location:- C:\Program Files (x86)\Common Files\Adobe\SLCache
• Delete all files inside the SLCache folder
• Go to the location:- C:\ProgramData\Adobe\SLStore
• Delete all files inside the SLStore folder
• Open FM again, in case you get the sign-in window means your device is deactivated.

In the latter scenario, I think it's the presence of the login window when you fire FM back up that indicates that it's been deactivated. If you run into any difficulties activating the new machine, contact them again - traditionally they've been quite good at handling moving licences around from machine to machine.