While B2B Handsfree doesn't offer a way for customers to change their VAT ID themselves, you can easily do it for them. The VAT ID is stored in a customer metafield and all you need to do to edit it is make it available in your store's admin.

Open the settings of your store and navigate to Custom data > Customers:

Then click on View unstructured metafields:

Click the Add definition button next to the entry a9design_b2breg.vatid:

Enter a name for the definition and select the type Single line text:

Leave all the other fields as-is and click Save.

Now head over to any customer that has a VAT ID and you'll see an input for the VAT ID:

Here you can edit the customer's VAT ID and any new orders the customer places will have the new VAT ID assigned to them.

You can also add a VAT ID to any customers the same way. Just enter it into the field and click Save.

Please note that the VAT ID is also stored in the notes field of the customer. It's only stored there for informational purposes, it's not used for invoices. But you'll want to change it there nevertheless.