How to move a record from one table to another?

Question

MySQL

Greetings!
I want to know how to copy data with replacement from one table to another correctly and without data loss.
Such a case, there are 2 schemas in one database from several interconnected tables by keys and a one-to-one relationship. . It is clear that this is a simple example. entities can be more complex and consist of multiple tables. The point is to transfer data to the public table without loss and failure, when there is a constant data sampling.
Use lock during fetch? Or is it enough to wrap it in a transaction?