How to update arry of string value from another colleciton

Dear all,
we have two collection A and B

i want to update collection B field C from collection A without effecting column NAME and CLASS
can we achieve this from query ? if not is there any other way to achieve this

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 and may be