Hi! Please clarify: you need to transfer website from one server to another without changing domain name, so you need to just transfer website hosting facilities?
If so, then you can find an answer in neighbouring topic:
https://captchaforum.com/threads/how-to-transfer-website-from-one-host-to-another.185/unread
In case you want to change the domain name, i. e. you have "mysite.com" and you want to move it to "mynewsite.net" - then we have a few possible situations.
1. You just want to change the domain without leaving the old one active. In this case all you actually need to do - is to unlink your old domain name from your current hosting and then link your new domain's DNS to your hosting. Note that old domain would not work anymore since it's not linked to any hosting.
You also would need to change all the links on your pages and in the database if you have absolute paths (like
https://mysite.com/picture1.jpg) and not relative ones (like //picture1.jpg).
2. More common situation is when you need to keep the old domain and hosting active in order to redirect your visitors to a new site. To make this you need to:
1) download all files and database of your website
2) update the links in the database and in the files (if you have absolute URLs)
3) move files and database to a new hosting
4) set up a 301 redirect for each of the pages on your old site to the corresponding page on your new domain name. This is important for telling Google that the page has moved to the new address. You can delete the content on the old site approx. after 1 month from finishing the moving.
5) put this in your old site's "robots.txt" file:
User-Agent: *
Disallow:
Host: new.name
6) After moving to your new domain name, you should tell Google that you’ve switched domains. You can do this with the Change of Address tool in the
Google Search Console.
7) Once you’re done moving, be sure to submit your new sitemap to Google. Google also recommends submitting the old sitemap that contains the forwarded URLs as well.
If you make everything right - you should get all of the old website's traffic and ratings in SE.