FEAT with a mixed design: Full-Model Setup

I have a mixed design where I have 4 conditions within subjects and 2 groups.
I ran the first-level in FEAT and defined my main effects and interactions of interest for each subject. Say I have 3 subjects in A and 3 in B. In the second-level, does it make sense to run only the subjects from A, leaving ‘Group’ in the Full-Model Setup set to 1 and running for each group separately, OR would it also make sens to run the second-level with participants from both groups and just set ‘Group’ to 1 or 2 in the model setup?

I thought the second-level was still averaging the copes within subjects…but was unsure if ‘Group’ referred to something else in the case of FEAT?

Follow-up question related to second-level analysis: why does a cope file not exist for the F-contrast from the first-level analysis?

Thanks in advanced!