This is a great example of a requirement that can be met by using Odoo Studio to customize Odoo. 

By creating a custom field and a smart button, you can do the following:

• enter the serial number of equipment not sold by you

• use Field Services to maintain that equipment

• see all visits over time for a specific serial number

Custom field:

1. From Field Services --> My Tasks --> Tasks, activate Odoo Studio

2. Click Views, then Form

3. Drag a New Many2one field to the Form (I put it under Project)

4. Related this field to the Lot/Serial model:

This gives you the ability to create a Serial Number prior to visiting, or during the visit, depending on when you learn of the Serial Number of the equipment you are looking after.

Smart Button:

1. From Inventory --> Products --> Lots/Serial Numbers, activate Odoo Studio

2. Click Views, then Form

3. Hover near the Location Smart Button until you see a PLUS icon:

4. Click the icon and add a Smart Button to show all Field Service visits:

This gives you the ability to show all Field Service Visits for a specific Serial Number.

Now, Users add the Serial to the Field Service Task:

They then enter the "product" for the Serial*:

They can add any model information in the Internal Reference field.  

When looking at the Serial Number in the Inventory App:

* Note that you can Archive the product if you don't want to see it in your Product Master data - and the inactive status can be defined as a default via context on the Lot/Serial field on the form (extra credit!) so that all products created via Field Services Tasks are archived automatically.