@dodo123
Here is a simple answer. Yes, the authority or ranking power of your current domain and all of your pages can be transfered to your new domain. There are a couple things you need to make sure happen during the transfer though. If you are just changing your domain name and not the content or design then it's not that difficult, but will require some careful attention to detail.

1. You must create a 301 redirect from every page of your current site to every corresponding page of the new domain name in order to maintain rankings of all of your pages.

Do not just point the old domain to your new domain as a whole it must be done on the page level.

Get your developer to help create 301 redirect file or on your server. Let me know if any questions www.brandliftdigital.com