Step 1 - From anywhere within your desired form group, click the hamburger menu icon at the top left of the page to open the navigation panel, and select Security Groups.

Alternatively, navigate to your desired form group's home page and select Security Groups.

Step 2 - Within the Security Groups page, locate the security group you wish to copy. Click the gear icon on the security's group's header, and...

...select the Copy Security Group option from the dropdown menu that appears.

Step 3 - A new window containing a block of text will pop up. Triple-click the text to highlight it, then copy it. Once you're finished, click the "X" at the upper-right corner of the window, or click Cancel in the bottom-right corner of the window.

Step 4 - Navigate to the Security Groups page of the form group you wish to copy into, and select Paste Security Group underneath the heading.

Step 5 - Another new window will open. Paste the text you copied earlier into the box labeled Paste Contents, then click the green Paste Security Group button at the bottom of the window.

A message will pop up asking for you to enter a new name for the security group, along with a new text box titled Pasted Security Group Name. The box will contain the name "{Original Group Name} - Copied" by default, but you can change this by modifying the text to the name you desire.

Step 6 - Once you are ready, click Paste Security Group again.

Your newly-copied security group should now be listed with the rest of your chosen form group's security groups!

See also: 

ATLAS FormBuilder - Adding a User to a Security Group