logo and favicon images not shown when changing site address

Hello, I’ve got some problems when moving my website from staging to production.
My staging site is staging1.adventurerooms.it, while the production site is http://www.adventurerooms.it
If I configure the logo and the favicon images in the staging site, the images url points to the staging site (absolute and not relative urls).
So, when I move the staging to production and delete the staging site, the logo and favicon images are missing.
Shouldn’t the theme save relatives urls so that moving the site from staging to production does not create this problem ?
Digging even more in the website I notice that all urls of images added with the page builder are saved as absolute urls, so all images are not displayed (missing) when moving from staging to production.
I would be very gratefull if you can help me address this problem
Thanks in advance
Antonio