During registration or new user there is no issue as the address fields are the same for information tab and CBSubs.

Both on backend and frontend the autoaction does not update the CBSubs fields in cbsubs_payment_baskets for the user.

I have tried both as a moderator from frontend or backend and as a user on frontend

So we're back to the old conflict basket/invoice

We need to update the table cbsubs_payment_baskets with the correct data for name/addresses, not only the _comprofiler table. For all recurring payments the data (name/address...) seems to be taken from the basket while the customer may have changed its data a couple of times during the recurring time.

This means that what you call invoices (baskets) are wrong after a time for all recurring payments.

Is there a way to update the correct data apart from a direct change in the cbsubs_payment_baskets table ?

Excellent idea, I forgot about query auto actions for this.

I think that this should be ok ?
But it will update all table rows. How could I simply update the last ones that exist at the time of the change ?
I think that changing the last existing invoice should be enough. Often customers complain that the last invoice arrived with the wrong address or person in charge in case of moves in the company.