yes, that's exactly one of the main purposes of Akeeba Backup.
First of all take a backup of your website: Akeeba Backup will create one (or more than one, depending by the size) archives that will contain all your site files and data. On top of that, a script for site restoration will be included.
Now download the new archives and upload it to your new staging server. There you can extract your archive using the Kickstart script, then run the restoration wizard that will let you specify all new details (database access details, filesystem path and new domain name). The restoration script will take care of updating all your data inside the database.
At the end of it, you have a new verbatim copy of the live website, where you can do all the tests you want. Once you're happy with the result, you have two options:
- Take a backup of the staging website and upload it to live
- Take note of the steps and any issues you had on the staging website and replicate them on the live site.
I personally suggest you to go with the second approach, since most likely new data will be placed on the live site while you're testing the new template (for example: orders).
That was just an overview of the whole process, I'd suggest you to take a look at our video tutorials so you'll know what to expect: https://www.akeebabackup.com/videos/1215-akeeba-backup-wordpress.html
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