Please provide actual sample source documents and sample result documents that we can import directly in our environment. Coming up with code is time consuming and it is double time consuming if we have to create our own documents that matches your description.
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Is it a one time thing? Something you want to automate whenever A changes?
The solution will likely involve https://docs.mongodb.com/manual/reference/operator/aggregation/merge/ and may be https://docs.mongodb.com/manual/changeStreams/.