Answer:
Steps to reproduce (*)
Create a customer account
Go to my account, and add a shipping address
2.5. Enable Persistent Shopping Cart (updated Oct 10.2019)
Add any product and go to the checkout !Impotent: wait until the customer session expires (one hour by default) but no longer than Persistence Lifetime is set to (updated Oct 10.2019)
3.5 Reload the page so that somewhere in the upper-right corner You get "Not You?" link next to the welcome message (updated Oct 10.2019)
3.6 Clik on "Not You?" enter the credentials of the customer and log in (updated Oct 10.2019)
3.6 Go to Mini Cart end press Precede to Checkout (updated Oct 10.2019)
Select the address you have just added
Select a shipping method and click next button