What you request is not a simple process. It can be done, but takes very careful work and can be quite tedious. You can update the table occurrence for one layout's customer table to make it refer to the customer table in another file, but the design of each customer table is not identical and can require updating each layout, script, and value list to refer to the correct field in the newly linked in table. You may also need to recreate field definitions from the customer table you are discarding in the table with which you are replacing it.
All of this requires a very thourough knowledge of FileMaker and how it works. FileMaker Advanced's script debugger and database design report can be extremely helpful throughout such a process.
You might investigate FileMaker Inc's Business Productivity Pack and see if provides an alternative set of template files where this type of common customer table may already have been set up.