Open your inventory file and select Manage | Database | Relationshps
Click the bottom left button to create a new table occurrence.
Select "add FileMaker Data Source" from the drop down menu in the dialog that appears.
First select your Contacts file, then select the Contacts table found inside of the contacts file as the data source for your table occurrence.
Then drag to link a field in Contacts to a field in the desired Table in Inventory to establish a relationship. You may need to define a new field in your inventory table to serve as the customer ID field.
This does what you request, but it's only the first step. You'd then need to add/change layouts in the Inventory file before you can see and edit data from contacts. Similar changes are likely needed for value lists, scripts and possibly other parts of your database. This is not a change to make unless you have a decent knowledge of how all parts of a FileMaker database file work.