RE: Outlook and Business central
It is not mandatory to use the same login for both, but it sure makes your life a lot more easier if you do so.
But i am not sure what you mean by sharing incoming documents from outlook. There is no functionality in the standard system that does that.
You can add user A as a guest user in the Azure AD that holds the Business Central tenant. That will at least make things easier for you.
If you are talking about using the outlook-add in for Business Central then you definitely should use the same log in.