Thank you very much for the response. My question is the following:

In the operations settings, there is an option called "Serial/Batch Numbers" with the following options:

Create new

Use existing

When activating the second option, which is when making the transfer from the parent company to the daughter branch, it lets me choose the serial number assigned from the parent branch, I get a warning error:

After clicking close, it lets me save it and accept the transfer, where it's reflected in the child branch's inventory.

When I try to return that item from the child branch to the parent branch, I get the same error, but when I click validate, it tells me there's another problem because it already exists and won't let me make the transfer.

Thanks

Thank you for your detailed follow-up.
You're absolutely right that selecting “Use Existing” under the Serial/Batch Numbers setting allows you to receive the serial number created by the parent company. However, the warning you're seeing is due to Odoo's default behavior of treating serial numbers (stock.production.lot) as company-specific.
Best Practice Going Forward
To ensure smooth intercompany transfers (including returns), and to maintain consistent serial number traceability across branches, the recommended solution is:
Customize Odoo to Make Serial Numbers Global
We can implement a small custom module that:

Removes the company restriction on serial numbers

Allows shared serial numbers across all companies

Prevents duplicate errors during returns or intercompany transfers

Ensures that a single serial number (like 0000019) is always recognized system-wide

This way, you won’t be forced to recreate or duplicate serial numbers, and returns from one branch to another will work without errors.

Are the transfers completed with a delivery and receipt operation or are they done with internal transfers?