How to display the same field in different modules and forms

I want to display an editable field from Module A and form A to Module B and form B. How do I go about doing it while retaining the information from Module A and form A?

It is not clear what you are calling “Module A” and “form A”.
But once a field is registered into a Model, it is accessible for this model in any module (but it creates the requirements to make this other module depends on the one defining the field).
On the views, the field is also available to any view of this model.