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After getting some suggestions on my AX Forum question, I started looking in the Main Accounts and their setup. When looking at the details of a Main Account, I found that the 'Companies' field was not auto-populating:
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If you hit that green '+' I can add my new entity, however, I would have expected it to be auto-populated. I also noticed that the Legal Entity in the Financial dimensions on the Main Account wasn't set either:
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As you can see in the image, I was able to set it with my new Entity, however, I would have expected it to be auto-populated after entity setup.
Possible Root Cause:
When setting up my entity I completed the setup in General ledger -> Setup -> Ledger before making the Entity a Virtual Company:
I believe that if you setup the Virtual Company first and then do these Ledger settings the items above will auto-populate.